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Title: Asplund Functions and Projectional Resolutions of the Identity
Authors: Zemek, Martin
Keywords: Asplund Function
Asplund Space
Weakly LindelÖf Determined Space
Projectional Resolution Of The Identity
Locally Uniformly Rotund Norm
Issue Date: 2000
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 26, No 4, (2000), 287p-308p
Abstract: 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.
Description: *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.
ISSN: 1310-6600
Appears in Collections:Volume 26 Number 4

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