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Title: Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps
Authors: Plichko, Anatolij
Keywords: Banach Space
Borel Map
Issue Date: 1997
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 23, No 3-4, (1997), 335p-350p
Abstract: 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. If a Banach space E cannot be decomposed into a direct sum of separable and reflexive subspaces, then there exists a normed space Z and a linear continuous bijective operator T : E → Z such that T^(−1) is not a Borel map.
Description: * This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95.
ISSN: 1310-6600
Appears in Collections:Volume 23 Number 3-4

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