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

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

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Authors: Plichko, Anatolij
Issue Date: 1997
Citation: Serdica Mathematical Journal, Vol. 23, No 3-4, (1997), 335p-350p Copy to clipboard
ISSN: 1310-6600
URI: http://hdl.handle.net/10525/591 Copy to clipboard
Note:

* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95.

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.
Language: en
Publisher: Institute of Mathematics and Informatics, Bulgarian Academy of SciencesSubject: Banach SpaceBorel Map
Type: Article