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|Title:||On small combination of slices in Banach spaces|
Rao, T. S. S. R. K.
|Keywords:||Small combination of slices;M-Ideals;Strict ideals;U-Subspaces;Pequeña combinación de sectores;Ideales- M;Ideales estrictos;Subespacios en U|
|Publisher:||Universidad de Extremadura|
|Abstract:||The notion of Small Combination of Slices (SCS) in the unit ball of a Banach space was first introduced in  and subsequently analyzed in detail in  and . 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.|
|Appears in Collections:||Extracta Mathematicae Vol. 31, nº 1 (2016)|
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