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

Plichko, Anatolij. "Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps." Serdica Mathematical Journal 23.3-4 (1997): 335-350. <http://eudml.org/doc/11621>.

@article{Plichko1997,
abstract = {* 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. 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.},
author = {Plichko, Anatolij},
journal = {Serdica Mathematical Journal},
keywords = {Banach Space; Borel Map; direct sum of separable and reflexive subspaces; linear continuous bijective operator; Borel map; continuum hypothesis},
language = {eng},
number = {3-4},
pages = {335-350},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps},
url = {http://eudml.org/doc/11621},
volume = {23},
year = {1997},
}

TY - JOUR
AU - Plichko, Anatolij
TI - Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps
JO - Serdica Mathematical Journal
PY - 1997
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 23
IS - 3-4
SP - 335
EP - 350
AB - * 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. 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.
LA - eng
KW - Banach Space; Borel Map; direct sum of separable and reflexive subspaces; linear continuous bijective operator; Borel map; continuum hypothesis
UR - http://eudml.org/doc/11621
ER -