Funktsionaalanalüüsi seminar | Tartu Ülikooli matemaatika ja statistika instituut

## TÜ üksuste kontaktandmed

Faculty phone:
737 5341
Jakobi 2, ruumid 116–121, 51014 Tartu
• valdkonna dekanaat
Faculty phone:
737 5341
Jakobi 2, ruumid 116–121, 51005 Tartu
• ajaloo ja arheoloogia instituut
Faculty phone:
737 5651
Jakobi 2, 51005 Tartu
Faculty phone:
737 5221
Jakobi 2, IV korrus, 51005 Tartu
• filosoofia ja semiootika instituut
Faculty phone:
737 5314
Jakobi 2, ruumid 309–352, 51005 Tartu
Faculty phone:
737 5223
Ülikooli 16, 51003 Tartu
• maailma keelte ja kultuuride kolledž
J. Liivi 4, 50409, Tartu
Faculty phone:
737 5300
Ülikooli 18-310, 50090 Tartu
Faculty phone:
435 5232
Posti 1, 71004 Viljandi
Faculty phone:
737 5957
Lossi 36, 51003 Tartu
• valdkonna dekanaat
Faculty phone:
737 5900
Lossi 36, 51003 Tartu
Faculty phone:
737 6440
Salme 1a–29, 50103 Tartu
• Johan Skytte poliitikauuringute instituut
Faculty phone:
737 5582
Lossi 36–301, 51003 Tartu
Faculty phone:
737 6310
Narva mnt 18, 51009 Tartu
• psühholoogia instituut
Faculty phone:
737 5902
Näituse 2, 50409 Tartu
Faculty phone:
737 5390
Näituse 20–324, 50409 Tartu
Faculty phone:
737 5188
Lossi 36, 51003 Tartu
• Narva kolledž
Faculty phone:
740 1900
Raekoja plats 2, 20307 Narva
• Pärnu kolledž
Faculty phone:
445 0520
Ringi 35, 80012 Pärnu
Faculty phone:
737 5326
Ravila 19, 50411 Tartu
• valdkonna dekanaat
Faculty phone:
737 5326
Ravila 19, 50411 Tartu
• bio- ja siirdemeditsiini instituut
Faculty phone:
737 4210
Biomeedikum, Ravila 19, 50411 Tartu
• farmaatsia instituut
Faculty phone:
737 5286
Nooruse 1, 50411 Tartu
Faculty phone:
731 9856
Raekoja plats 6, 51003 Tartu
• kliinilise meditsiini instituut
Faculty phone:
737 5323
L. Puusepa 8, 50406 Tartu
• peremeditsiini ja rahvatervishoiu instituut
Faculty phone:
737 4190
Ravila 19, 50411 Tartu
Faculty phone:
737 5360
Jakobi 5–205, 51005 Tartu
Faculty phone:
737 5820
Vanemuise 46–208, 51014 Tartu
• valdkonna dekanaat
Faculty phone:
737 5820
Vanemuise 46–208, 51003 Tartu
Faculty phone:
737 5445
Narva mnt 18, 51009 Tartu
• genoomika instituut
Faculty phone:
737 4000
Riia 23b, 51010 Tartu
• Eesti mereinstituut
Faculty phone:
671 8902
Mäealuse 14, 12618 Tallinn
• füüsika instituut
W. Ostwaldi 1, 50411 Tartu
• keemia instituut
Faculty phone:
737 5261
Ravila 14a, 50411 Tartu
• matemaatika ja statistika instituut
Faculty phone:
737 5860
Narva mnt 18, 51009 Tartu
• molekulaar- ja rakubioloogia instituut
Faculty phone:
737 5027
Riia 23, 23b–134, 51010 Tartu
• Tartu observatoorium
Faculty phone:
737 4510
Observatooriumi 1, Tõravere, 61602 Tartumaa
• tehnoloogiainstituut
Faculty phone:
737 4800
Nooruse 1, 50411 Tartu
Faculty phone:
737 5835
Vanemuise 46, 51003 Tartu
Asutused
• raamatukogu
Faculty phone:
737 5702
W. Struve 1, 50091 Tartu
Faculty phone:
737 5581
Uppsala 10, 51003 Tartu
• muuseum
Faculty phone:
737 5674
Lossi 25, 51003 Tartu
• loodusmuuseum ja botaanikaaed
Faculty phone:
737 6076
Vanemuise 46, 51003 Tartu
Tugiüksused
• ettevõtlus- ja innovatsioonikeskus
Faculty phone:
737 4809
Narva mnt 18, 51009, Tartu
• grandikeskus
Faculty phone:
737 6215
Raekoja plats 9, 51004 Tartu
• hankeosakond
Faculty phone:
737 6632
Ülikooli 18a, 51005 Tartu
• infotehnoloogia osakond
Faculty phone:
737 6000, arvutiabi: 737 5500
Ülikooli 18a, 51005 Tartu
• kantselei
Faculty phone:
737 5606
Ülikooli 18a, 51005 Tartu
• kinnisvaraosakond
Faculty phone:
737 5137
Ülikooli 18a, 51005 Tartu
• kirjastus
Faculty phone:
+372 737 5945
W. Struve 1, 50091 Tartu
• personaliosakond
Faculty phone:
737 5145
Ülikooli 18, ruumid 302 ja 304, 50090 Tartu
• rahandusosakond
Faculty phone:
737 5125
Jakobi 4, 51005 Tartu
• rahvusvahelise koostöö ja protokolli osakond
Faculty phone:
737 6123
Ülikooli 18, ruumid 104, 304, 305, 50090 Tartu
Faculty phone:
737 5600
Ülikooli 18, 51014 Tartu
• siseauditi büroo
Ülikooli 18–244, 51005 Tartu
• Tallinna esindus
Faculty phone:
737 6600
Teatri väljak 3, 10143 Tallinn
• turundus- ja kommunikatsiooniosakond
Faculty phone:
737 5687
Ülikooli 18, ruumid 102, 104, 209, 210, 50090 Tartu
• õppeosakond
Faculty phone:
737 5620
Ülikooli 18, 50090 Tartu
• üliõpilasesindus
Ülikooli 18b, 51005 Tartu
Muud üksused
• MTÜ Tartu Ülikooli Akadeemiline Spordiklubi
Faculty phone:
737 5371
Ujula 4, 51008 Tartu
Faculty phone:
740 9959
Narva mnt 25, 51013 Tartu
• MTÜ Tartu Üliõpilasmaja
Faculty phone:
730 2400
Kalevi 24, Tartu
• SA Tartu Ülikooli Kliinikum
Faculty phone:
731 8111
L. Puusepa 1a, 50406 Tartu
• Tartu Ülikooli Sihtasutus
Faculty phone:
737 5852
Ülikooli 18a–106, Tartu

## TÜ üksuste kontaktandmed

Faculty phone:
737 5341
Jakobi 2, ruumid 116–121, 51014 Tartu
• valdkonna dekanaat
Faculty phone:
737 5341
Jakobi 2, ruumid 116–121, 51005 Tartu
• ajaloo ja arheoloogia instituut
Faculty phone:
737 5651
Jakobi 2, 51005 Tartu
Faculty phone:
737 5221
Jakobi 2, IV korrus, 51005 Tartu
• filosoofia ja semiootika instituut
Faculty phone:
737 5314
Jakobi 2, ruumid 309–352, 51005 Tartu
Faculty phone:
737 5223
Ülikooli 16, 51003 Tartu
• maailma keelte ja kultuuride kolledž
J. Liivi 4, 50409, Tartu
Faculty phone:
737 5300
Ülikooli 18-310, 50090 Tartu
Faculty phone:
435 5232
Posti 1, 71004 Viljandi
Faculty phone:
737 5957
Lossi 36, 51003 Tartu
• valdkonna dekanaat
Faculty phone:
737 5900
Lossi 36, 51003 Tartu
Faculty phone:
737 6440
Salme 1a–29, 50103 Tartu
• Johan Skytte poliitikauuringute instituut
Faculty phone:
737 5582
Lossi 36–301, 51003 Tartu
Faculty phone:
737 6310
Narva mnt 18, 51009 Tartu
• psühholoogia instituut
Faculty phone:
737 5902
Näituse 2, 50409 Tartu
Faculty phone:
737 5390
Näituse 20–324, 50409 Tartu
Faculty phone:
737 5188
Lossi 36, 51003 Tartu
• Narva kolledž
Faculty phone:
740 1900
Raekoja plats 2, 20307 Narva
• Pärnu kolledž
Faculty phone:
445 0520
Ringi 35, 80012 Pärnu
Faculty phone:
737 5326
Ravila 19, 50411 Tartu
• valdkonna dekanaat
Faculty phone:
737 5326
Ravila 19, 50411 Tartu
• bio- ja siirdemeditsiini instituut
Faculty phone:
737 4210
Biomeedikum, Ravila 19, 50411 Tartu
• farmaatsia instituut
Faculty phone:
737 5286
Nooruse 1, 50411 Tartu
Faculty phone:
731 9856
Raekoja plats 6, 51003 Tartu
• kliinilise meditsiini instituut
Faculty phone:
737 5323
L. Puusepa 8, 50406 Tartu
• peremeditsiini ja rahvatervishoiu instituut
Faculty phone:
737 4190
Ravila 19, 50411 Tartu
Faculty phone:
737 5360
Jakobi 5–205, 51005 Tartu
Faculty phone:
737 5820
Vanemuise 46–208, 51014 Tartu
• valdkonna dekanaat
Faculty phone:
737 5820
Vanemuise 46–208, 51003 Tartu
Faculty phone:
737 5445
Narva mnt 18, 51009 Tartu
• genoomika instituut
Faculty phone:
737 4000
Riia 23b, 51010 Tartu
• Eesti mereinstituut
Faculty phone:
671 8902
Mäealuse 14, 12618 Tallinn
• füüsika instituut
W. Ostwaldi 1, 50411 Tartu
• keemia instituut
Faculty phone:
737 5261
Ravila 14a, 50411 Tartu
• matemaatika ja statistika instituut
Faculty phone:
737 5860
Narva mnt 18, 51009 Tartu
• molekulaar- ja rakubioloogia instituut
Faculty phone:
737 5027
Riia 23, 23b–134, 51010 Tartu
• Tartu observatoorium
Faculty phone:
737 4510
Observatooriumi 1, Tõravere, 61602 Tartumaa
• tehnoloogiainstituut
Faculty phone:
737 4800
Nooruse 1, 50411 Tartu
Faculty phone:
737 5835
Vanemuise 46, 51003 Tartu
Asutused
• raamatukogu
Faculty phone:
737 5702
W. Struve 1, 50091 Tartu
Faculty phone:
737 5581
Uppsala 10, 51003 Tartu
• muuseum
Faculty phone:
737 5674
Lossi 25, 51003 Tartu
• loodusmuuseum ja botaanikaaed
Faculty phone:
737 6076
Vanemuise 46, 51003 Tartu
Tugiüksused
• ettevõtlus- ja innovatsioonikeskus
Faculty phone:
737 4809
Narva mnt 18, 51009, Tartu
• grandikeskus
Faculty phone:
737 6215
Raekoja plats 9, 51004 Tartu
• hankeosakond
Faculty phone:
737 6632
Ülikooli 18a, 51005 Tartu
• infotehnoloogia osakond
Faculty phone:
737 6000, arvutiabi: 737 5500
Ülikooli 18a, 51005 Tartu
• kantselei
Faculty phone:
737 5606
Ülikooli 18a, 51005 Tartu
• kinnisvaraosakond
Faculty phone:
737 5137
Ülikooli 18a, 51005 Tartu
• kirjastus
Faculty phone:
+372 737 5945
W. Struve 1, 50091 Tartu
• personaliosakond
Faculty phone:
737 5145
Ülikooli 18, ruumid 302 ja 304, 50090 Tartu
• rahandusosakond
Faculty phone:
737 5125
Jakobi 4, 51005 Tartu
• rahvusvahelise koostöö ja protokolli osakond
Faculty phone:
737 6123
Ülikooli 18, ruumid 104, 304, 305, 50090 Tartu
Faculty phone:
737 5600
Ülikooli 18, 51014 Tartu
• siseauditi büroo
Ülikooli 18–244, 51005 Tartu
• Tallinna esindus
Faculty phone:
737 6600
Teatri väljak 3, 10143 Tallinn
• turundus- ja kommunikatsiooniosakond
Faculty phone:
737 5687
Ülikooli 18, ruumid 102, 104, 209, 210, 50090 Tartu
• õppeosakond
Faculty phone:
737 5620
Ülikooli 18, 50090 Tartu
• üliõpilasesindus
Ülikooli 18b, 51005 Tartu
Muud üksused
• MTÜ Tartu Ülikooli Akadeemiline Spordiklubi
Faculty phone:
737 5371
Ujula 4, 51008 Tartu
Faculty phone:
740 9959
Narva mnt 25, 51013 Tartu
• MTÜ Tartu Üliõpilasmaja
Faculty phone:
730 2400
Kalevi 24, Tartu
• SA Tartu Ülikooli Kliinikum
Faculty phone:
731 8111
L. Puusepa 1a, 50406 Tartu
• Tartu Ülikooli Sihtasutus
Faculty phone:
737 5852
Ülikooli 18a–106, Tartu

# Funktsionaalanalüüsi seminar

Narva mnt 18-2039 kell 10.00-12.00 (GMT+3)

Zoomiruum: https://ut-ee.zoom.us/j/95229664082?pwd=cmZNVEJSMFhkeWxlRXNEaVB3Umhpdz09
ID: 952 2966 4082
Parool: 261772

Millal Esineja Teema
06.06.2021 Mingu Jung
29.04.2021 Katriin Pirk (University of Tartu, Estonia) https://arxiv.org/abs/2012.09492
22.04.2021
NB! kell 11.00
Miguel Martín (University of Granada, Spain)

### Slicely Countably determined sets

15.04.2021 kell 12.00 Luis C. García Lirola (University of Zaragoza, Spain)

### The Weak Maximizing Property and asymptotic geometry of Banach spaces

Recently, a new property related to norm-attaining operators between Banach spaces has been introduced: the weak maximizing property (WMP). In this talk, we provide new sufficient conditions, based on the moduli of asymptotic uniform smoothness and convexity, which imply that a pair (X,Y) enjoys the WMP. This approach not only allows us to (re)obtain as a direct consequence that the pair has the WMP, but also provides many more natural examples of pairs having a given maximizing property. This is part of a joint work with Colin Petitjean.

08.04.2021 Nikita Leo (University of Tartu, Estonia)

### Plasticity of the unit ball of c0

In this talk we consider a challenging open problem of whether the unit ball of every Banach space is a plastic metric space (a metric space is called plastic if every non-expansive bijection from this space onto itself is an isometry). We are going to provide some insight into the problem and show what has been achieved so far. We also present a new result, which says that the unit ball of c0 has a property similar to plasticity - we show that a non-expansive bijection from the unit ball of c0 onto itself is an isometry, provided that the inverse map is continuous.

01.04.2021 Hyung-Joon Tag (Dongguk University, Republic of Korea)

Diameter two properties in some vector-valued function spaces

In this talk, we introduce the space A(K,Xover a uniform algebra on a compact Hausdorff space K. Every nonempty relatively weakly open subset of the unit ball of a vector-valued function space A(K,Xover an infinite dimensional uniform algebra has the diameter two. If X is uniformly convex, under the additional assumption of AXA(K,X), we show that Daugavet points and Δ-points on A(K,Xover a uniform algebra A are the same, and they are characterized by the norm-attainment at a limit point of the Shilov boundary of A. In addition, a sufficient condition for the convex diametral local diameter two property of A(K,Xis also provided.

25.03.2021 Alicia Quero de la Rosa

Numerical index with respect to an operator

The concept of numerical index was introduced by Lumer in 1968 in the context of the study and classification of operator algebras. This is a constant relating the norm and the numerical range of bounded linear operators on the space. More precisely, the numerical index of a Banach space X, n(X), is the greatest constant k0 such that kTsup{|x(Tx)|:xX,xX,x=x=x(x)=1for every TL(X).

Recently, Ardalani introduced new concepts of numerical range, numerical radius, and numerical index, which generalize in a natural way the classical ones and allow to extend the setting to the context of operators between possibly different Banach spaces. Given a norm-one operator GL(X,Y) between two Banach spaces X and Y, the numerical index with respect to GnG(X,Y), is the greatest constant ksuch that kTinfδ>0sup{|y(Tx)|:yY,xX,y=x=1,Rey(Gx)>1δfor every TL(X,Y).

In this talk, we will give an overview of the topic, analysing differences and similarities between these concepts, and presenting some classical and recent results in the area.

18.03.2021 Tomasso Russo (Czech Academy of Sciences, Czech Technical University in Prague)

(1+)-meters apart: Separated sets in Covid times

Riesz’ lemma, one of the most classical results in Functional Analysis and now proved in the first lectures of every course in the topic, asserts that the unit sphere of every infinite-dimensional Banach space contains a sequence of points whose mutual distances are at least 1, thereby demonstrating the non-compactness of the unit ball in infinite dimensions. The, by now rather wide, topic of separated sets in Banach spaces can be safely considered to originate from such a lemma.

In our talk, we will survey some classical and recent results in the area, also pointing out some problems that remain open. We shall discuss the main ideas behind the proofs of selected results, as an illustration of some techniques in the area (both in the separable and the non-separable contexts). The talk is intended to be elementary and students-friendly, the unique real prerequisites being the definition of a Banach space and the Hahn–Banach theorem.

11.03.2021 Rubén Medina (University of Granada, Spain; Czech Technical University in Prague, Czech Republic)

A characterization of the weak topology of the unit ball of purely atomic preduals

We study Banach spaces with a weak stable unit ball, that is, Banach spaces where every convex combination of relatively weakly open subsets of the unit ball is again relatively weakly open in its unit ball. A walkthrough of previous overall results will be done, as well as a more concise dedication to the newer results. The main result of the talk will be a characterization of the spaces with weak stable unit ball among the -preduals.

04.03.2021 Stefano Ciaci (University of Tartu, Estonia)

A characterization of Banach spaces containing via ball-covering properties

Abstract. In 1989, G. Godefroy proved that a Banach space contains an isomorphic copy of  if and only if it can be equivalently renormed to be octahedral. It is known that octahedral norms can be characterized by means of covering the unit sphere by a finite number of balls. This observation allows us to connect the theory of octahedral norms with ball-covering properties of Banach spaces introduced by L. Cheng in 2006. Following this idea, we extend G. Godefroy’s result to higher cardinalities. We prove that, for an infinite cardinal κ, a Banach space X contains an isomorphic copy of if and only if it can be equivalently renormed in such a way that its unit sphere cannot be covered by κ many open balls not containing where α(0,1). We also investigate the relation between ball-coverings of the unit sphere and octahedral norms in the setting of higher cardinalities.

25.02.2021 Antonio Pérez Hernández (UNED, Spain)

Spear operators between Banach spaces

Abstract. The concept of spear operator is intimately related to the notions of numerical range, numerical radius and numerical index introduced for Banach spaces by Lumer and Bauer (1960s). Duncan et al. (1970s) showed that Banach spaces X having are characterized as those satisfying that for every TL(X) there is a modulus-one scalar θ such that

IdX+θT=1+T,

also providing the first examples and properties. The geometrical properties of these spaces have been extensively studied, searching for characterizations that do not involve operators, and leading to the introduction of new properties (lushness, alternative Daugavet property…) that have become useful in other settings.

More recently, Ardalani (2014) presented more general definitions of numerical range, numerical radius and numerical index in the context of operators between possibly different Banach spaces. In particular, he introduced the concept of and initiated the study of general spear operators: a norm-one operator GL(X,Y) between two (real or complex) Banach spaces X,Y is said to be a if for every TL(X,Y) there exists a modulus-one scalar θ such that

G+θT=1+T.

In this talk, we will give an overview of the topic, reviewing main results and ideas, and posing some open problems on the way.

04.12.2020 Abraham Rueda Zoca (University of Murcia, Spain)

$\mathrm{\Delta }$$\mathrm{}$$$- and Daugavet points in Lipschitz-free spaces

Abstract. In this talk we will focus on giving necessary and sufficient conditions for a Lipschitz-free spaces F(M) to have Δ- and Daugavet points. As a consequence of our study, we will provide examples of metric spaces M and molecules in F(M) which are Δ-points but not Daugavet points, which is a completely different behaviour to the case of -spaces. We end with some open questions.

Video

27.11.2020 Elisa Regina dos Santos (Federal University of Uberlândia, Brazil)

Polynomial Daugavet Centers

Video

20.11.2020 Olesia Zavarzina (V.N. Karazin Kharkiv National University, Ukraine)

Generalized-lush spaces and connected problems

Abstract. The talk is devoted to geometric properties of GL-spaces. We will demonstrate that every finite-dimensional GL-space is polyhedral; We also characterise the spaces with absolute norm such that for every finite collection of GL-spaces their E-sum is a GL-space (GL-respecting spaces). We will also give the classification of GL- and GLR-spaces in dimention 2.

Video

13.11.2020

Sheldon Dantas (Czech Technical University in Prague, Czech Republic)

Gonzalo Martínez Cervantes (University of Murcia, Spain)

Octahedral norms in Free Banach Lattices

Abstract. Our aim in this talk is twofold. First of all, we present an overview on basic facts about free Banach lattices generated by a given Banach space E, which will be denoted by FBL[E]. We present some properties and known results about such a space. This will give all the necessary background we need for the second part of the talk, which consists on the study of octahedral norms in FBL[E]. We provide some sufficient conditions so that such a space has an octahedral norm. We also discuss almost squareness and Fréchet differentiability on these spaces. We conclude the talk by presenting some natural questions related to the Daugavet property.

Video
23.10.2020 André Martiny (University of Agder, Norway)

Daugavet- and delta-points in Banach spaces with unconditional bases

Abstract. We study the existence of Daugavet- and delta-points in the unit sphere of Banach spaces with a 1-unconditional basis. A norm one element x in a Banach space is a Daugavet-point (resp. delta-point) if every element in the unit ball (resp. x itself) is in the closed convex hull of unit ball elements that are almost at distance 2 from x. A Banach space has the Daugavet property (resp. diametral local diameter two property) if and only if every norm one element is a Daugavet-point (resp. delta-point). It is well-known that a Banach space with the Daugavet property does not have an unconditional basis. Similarly spaces with the diametral local diameter two property do not have an unconditional basis with suppression unconditional constant strictly less than 2.

We show that no Banach space with a subsymmetric basis can have delta-points. In contrast we construct a Banach space with a 1-unconditional basis with delta-points, but with no Daugavet-points, and a Banach space with a 1-unconditional basis with a unit ball in which the Daugavet-points are weakly dense.