# Asplund Functions and Projectional Resolutions of the Identity

• Volume: 26, Issue: 4, page 287-308
• ISSN: 1310-6600

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## Abstract

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*Supported by the Grants AV ˇCR 101-97-02, 101-90-03, GA ˇCR 201-98-1449, and by the Grant of the Faculty of Civil Engineering of the Czech Technical University No. 2003.We further develop the theory of the so called Asplund functions, recently introduced and studied by W. K. Tang. Let f be an Asplund function on a Banach space X. We prove that (i) the subspace Y := sp ∂f(X) has a projectional resolution of the identity, and that (ii) if X is weakly Lindel¨of determined, then X admits a projectional resolution of the identity such that the adjoint projections restricted to Y form a projectional resolution of the identity on Y , and the dual X* admits an equivalent dual norm such that its restriction to Y is locally uniformly rotund.

## How to cite

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Zemek, Martin. "Asplund Functions and Projectional Resolutions of the Identity." Serdica Mathematical Journal 26.4 (2000): 287-308. <http://eudml.org/doc/11495>.

@article{Zemek2000,
abstract = {*Supported by the Grants AV ˇCR 101-97-02, 101-90-03, GA ˇCR 201-98-1449, and by the Grant of the Faculty of Civil Engineering of the Czech Technical University No. 2003.We further develop the theory of the so called Asplund functions, recently introduced and studied by W. K. Tang. Let f be an Asplund function on a Banach space X. We prove that (i) the subspace Y := sp ∂f(X) has a projectional resolution of the identity, and that (ii) if X is weakly Lindel¨of determined, then X admits a projectional resolution of the identity such that the adjoint projections restricted to Y form a projectional resolution of the identity on Y , and the dual X* admits an equivalent dual norm such that its restriction to Y is locally uniformly rotund.},
author = {Zemek, Martin},
journal = {Serdica Mathematical Journal},
keywords = {Asplund Function; Asplund Space; Weakly LindelÖf Determined Space; Projectional Resolution Of The Identity; Locally Uniformly Rotund Norm; Asplund function; locally uniformly rotund norm; Asplund space; weakly Lindelöf determined space; projectional resolution of the identity},
language = {eng},
number = {4},
pages = {287-308},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Asplund Functions and Projectional Resolutions of the Identity},
url = {http://eudml.org/doc/11495},
volume = {26},
year = {2000},
}

TY - JOUR
AU - Zemek, Martin
TI - Asplund Functions and Projectional Resolutions of the Identity
JO - Serdica Mathematical Journal
PY - 2000
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 26
IS - 4
SP - 287
EP - 308
AB - *Supported by the Grants AV ˇCR 101-97-02, 101-90-03, GA ˇCR 201-98-1449, and by the Grant of the Faculty of Civil Engineering of the Czech Technical University No. 2003.We further develop the theory of the so called Asplund functions, recently introduced and studied by W. K. Tang. Let f be an Asplund function on a Banach space X. We prove that (i) the subspace Y := sp ∂f(X) has a projectional resolution of the identity, and that (ii) if X is weakly Lindel¨of determined, then X admits a projectional resolution of the identity such that the adjoint projections restricted to Y form a projectional resolution of the identity on Y , and the dual X* admits an equivalent dual norm such that its restriction to Y is locally uniformly rotund.
LA - eng
KW - Asplund Function; Asplund Space; Weakly LindelÖf Determined Space; Projectional Resolution Of The Identity; Locally Uniformly Rotund Norm; Asplund function; locally uniformly rotund norm; Asplund space; weakly Lindelöf determined space; projectional resolution of the identity
UR - http://eudml.org/doc/11495
ER -

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