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Monday, February 2, 2015 -
11:30 to 12:30
Dr. Sudeshna Basu
George Washington University, USA
Stability of ball properties in Banach spaces
Abstract: In this work, we study certain stability results for Ball Separation Porperties in Banach Spaces leading to a discussion in the context of operator spaces. In this work, we study certain stability results for Small Comibiantion of Slices Property (SCSP) leading to a discussion on SCSP in the context of operator spaces. SCS points were first introduced in [GGMS] as a “slice generalisation” of the PC (i.e. point of continuity points for which the identity mapping from weak topology to norm topology is continuous.) It was proved in [GGMS] that Xis strongly regular ( respectively $X^∗$ is $w^∗$-strongly regular) if and only if every non empty bounded convex set K in X ( respectively K in $X^∗$) is contained in the norm closure ( respectively $w^∗$-closure) of SCS(K)( respectively $w^∗$-SCS(K)) i.e. the SCS points ($w^∗$- SCS points) of K. Later, it was proved in [S] that a Banach space has Radon Nikodym Property (RNP) if and only if it is strongly regular and it has the Krien Milamn Property(KMP). Subsequently, the concepts of SCS points was used in [R] to investigate the structure of non dentable closed bounded convex sets in Banach spaces. The “point version” of the result in [S] ( i.e. charesterisation of RNP ),was also shown to be true in [HL] which extends the results in [LLT].

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