Diameter two properties in some vector-valued function spacesd
In this talk, we introduce the space A(K,X) over a uniform algebra A on a compact Hausdorff space K. Every nonempty relatively weakly open subset of the unit ball of a vector-valued function space A(K,X) over an infinite dimensional uniform algebra has the diameter two. If X is uniformly convex, under the additional assumption of A⊗X⊂A(K,X), we show that Daugavet points and Δ-points on A(K,X) over 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,X) is also provided.
1. aprillil kell 10:00. Liitu Zoomis.
ID: 952 2966 4082
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