Slicely countably determined sets, spaces, and operators
Miguel Martín (University of Granada, Spain)
Slicely countably determined spaces (SCD spaces) were introduced by Aviles, Kadets, Martin, Meri, and Shepelska (Transactions of the American Mathematical Society 2010) as a topological property for separable Banach spaces which is satisfied by both Asplund spaces and spaces with the RNP (actually, by both spaces not containing and strongly regular spaces). The property is defined in terms of a property of the slices of convex bounded subsets and produce interesting classes of bounded linear operators (SCD and HSCD operators). These ideas have been successfully applied to get important consequences in the theory of numerical index one spaces, for the Daugavet property, and for the study of spear operators between Banach spaces.
The objective of this seminar is to present the main examples and applications of the theory, comment some recent developments and present some open problems.
Some related references are the following ones:
- Aviles, Martin, Meri, Shepelska. Slicely countably determined Banach spaces. Trans. Amer. Math. Soc. 362 (2010), 4871–4900.
- Kadets, Martin, Meri, Perez. Spear operators between Banach spaces. Lecture Notes in Math. 2205, 2018.
- Kadets, Perez, Werner. Operations with slicely countably determined sets, Funct. Approx. 59 (2018), 77–98.
22. aprillil kell 11.00. Liitu Zoomis.
ID: 952 2966 4082
Rohkem infot funktsionaalanalüüsi seminaride kohta siin.