On small combination of slices in Banach spaces

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On small combination of slices in Banach spaces

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Title: On small combination of slices in Banach spaces
Author: Basu, Sudeshna; Rao, T. S. S. R. K.
Abstract: The notion of Small Combination of Slices (SCS) in the unit ball of a Banach space was first introduced in [4] and subsequently analyzed in detail in [12] and [13]. In this work, we introduce the notion of BSCSP, which can be seen as a generalization of dentability in terms of SCS. We study certain stability results for the w*-BSCSP leading to a discussion on BSCSP in the context of ideals of Banach spaces. We prove that the w*-BSCSP can be lifted from a M-ideal to the whole Banach Space. We also prove similar results for strict ideals and U-subspaces of a Banach space. We note that the space C(K;X)* has w*-BSCSP when K is dispersed and X* has the w*-BSCSP.
URI: http://hdl.handle.net/10662/8996
Date: 2016

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