A converse to Amir-Lindenstrauss theorem in complex Banach spaces.

Ondrej F. K. Kalenda

RACSAM (2006)

  • Volume: 100, Issue: 1-2, page 183-190
  • ISSN: 1578-7303

Abstract

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We show that a complex Banach space is weakly Lindelöf determined if and only if the dual unit ball of any equivalent norm is weak* Valdivia compactum. We deduce that a complex Banach space X is weakly Lindelöf determined if and only if any nonseparable Banach space isomorphic to a complemented subspace of X admits a projectional resolution of the identity. These results complete the previous ones on real spaces.

How to cite

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Kalenda, Ondrej F. K.. "A converse to Amir-Lindenstrauss theorem in complex Banach spaces.." RACSAM 100.1-2 (2006): 183-190. <http://eudml.org/doc/41651>.

@article{Kalenda2006,
abstract = {We show that a complex Banach space is weakly Lindelöf determined if and only if the dual unit ball of any equivalent norm is weak* Valdivia compactum. We deduce that a complex Banach space X is weakly Lindelöf determined if and only if any nonseparable Banach space isomorphic to a complemented subspace of X admits a projectional resolution of the identity. These results complete the previous ones on real spaces.},
author = {Kalenda, Ondrej F. K.},
journal = {RACSAM},
keywords = {weakly Lindelöf determined space; Valdivia compact; projectional resolution of the identity},
language = {eng},
number = {1-2},
pages = {183-190},
title = {A converse to Amir-Lindenstrauss theorem in complex Banach spaces.},
url = {http://eudml.org/doc/41651},
volume = {100},
year = {2006},
}

TY - JOUR
AU - Kalenda, Ondrej F. K.
TI - A converse to Amir-Lindenstrauss theorem in complex Banach spaces.
JO - RACSAM
PY - 2006
VL - 100
IS - 1-2
SP - 183
EP - 190
AB - We show that a complex Banach space is weakly Lindelöf determined if and only if the dual unit ball of any equivalent norm is weak* Valdivia compactum. We deduce that a complex Banach space X is weakly Lindelöf determined if and only if any nonseparable Banach space isomorphic to a complemented subspace of X admits a projectional resolution of the identity. These results complete the previous ones on real spaces.
LA - eng
KW - weakly Lindelöf determined space; Valdivia compact; projectional resolution of the identity
UR - http://eudml.org/doc/41651
ER -

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