Asplund Functions and Projectional Resolutions of the Identity
Serdica Mathematical Journal, Tome 26 (2000) no. 4, pp. 287-308
Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library
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.
Keywords:
Asplund Function, Asplund Space, Weakly LindelÖf Determined Space, Projectional Resolution Of The Identity, Locally Uniformly Rotund Norm
@article{SMJ2_2000_26_4_a1,
author = {Zemek, Martin},
title = {Asplund {Functions} and {Projectional} {Resolutions} of the {Identity}},
journal = {Serdica Mathematical Journal},
pages = {287--308},
publisher = {mathdoc},
volume = {26},
number = {4},
year = {2000},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SMJ2_2000_26_4_a1/}
}
Zemek, Martin. Asplund Functions and Projectional Resolutions of the Identity. Serdica Mathematical Journal, Tome 26 (2000) no. 4, pp. 287-308. http://geodesic.mathdoc.fr/item/SMJ2_2000_26_4_a1/