# Asplund Functions and Projectional Resolutions of the Identity

Serdica Mathematical Journal (2000)

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

## Access Full Article

top## Abstract

top## How to cite

topZemek, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.