Displaying similar documents to “Ordinal indices in Banach spaces.”

Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps

Plichko, Anatolij (1997)

Serdica Mathematical Journal

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* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95. The main results of the paper are: Theorem 1. Let a Banach space E be decomposed into a direct sum of separable and reflexive subspaces. Then for every Hausdorff locally convex topological vector space Z and for every linear continuous bijective operator T : E → Z, the inverse T^(−1) is a Borel map. Theorem 2. Let us assume the continuum hypothesis....

Partial unconditionality of weakly null sequences.

Jordi López Abad, Stevo Todorcevic (2006)

RACSAM

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We survey a combinatorial framework for studying subsequences of a given sequence in a Banach space, with particular emphasis on weakly-null sequences. We base our presentation on the crucial notion of introduced long time ago by Nash-Williams. In fact, one of the purposes of this survey is to isolate the importance of studying mappings defined on barriers as a crucial step towards solving a given problem that involves sequences in Banach spaces. We focus our study on various forms...

Strong proximinality and polyhedral spaces.

Gilles Godefroy, V. Indumathi (2001)

Revista Matemática Complutense

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In any dual space X*, the set QP of quasi-polyhedral points is contained in the set SSD of points of strong subdifferentiability of the norm which is itself contained in the set NA of norm attaining functionals. We show that NA and SSD coincide if and only if every proximinal hyperplane of X is strongly proximinal, and that if QP and NA coincide then every finite codimensional proximinal subspace of X is strongly proximinal. Natural examples and applications are provided.