IMI-BAS
 

BulDML at Institute of Mathematics and Informatics >
IMI >
IMI Periodicals >
Serdica Mathematical Journal >
1997 >
Volume 23 Number 3-4 >

Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/591

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.
URI: http://hdl.handle.net/10525/591
ISSN: 1310-6600
Appears in Collections:Volume 23 Number 3-4

Files in This Item:

File Description SizeFormat
sjm-vol23-num3-4-1997-p335-p350.pdf500.61 kBAdobe PDFView/Open

 



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

 

Valid XHTML 1.0! DSpace Software Copyright © 2002-2009  The DSpace Foundation - Feedback