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

Serdica Mathematical Journal (1997)

- Volume: 23, Issue: 3-4, page 335-350
- ISSN: 1310-6600

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topPlichko, 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 -

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