Title: Small Combination of Slices in Banach Spaces
Speaker: Dr. Sudeshna Basu (George Washington University)
Date: 10 June 2015
Time: 3.00 p.m.
Venue: LH I, Department of Mathematics
Abstract : In this work, we study certain stability results for Ball Separationproperties in Banach Spaces leading to a discussion in the context of operator spaces. In this work, we study certain stability results for Small Combination of Slices Property (SCSP) leading to a discussion on SCSP in the context of operator spaces. SCSpoints were first introduced as a slice generalisation of the PC (i.e. point ofcontinuity points for which the identity mapping from weak topology to normtopology is continuous.) It is known that X is strongly regular respectively Xis 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 that a Banach space has Radon- Nikodym Property (RNP) if and only if it is strongly regular and it has the Krein-Milamn Property(KMP). Subsequently, the concepts of SCS points was used to investigate the structure of non-dentable closed bounded convex sets in Banach spaces. The point version of the result was also shown to be true .