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

RACSAM (2006)

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

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topKalenda, 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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