Geodesic
Asplund Functions and Projectional Resolutions of the Identity
Serdica Mathematical Journal, Tome 26 (2000) no. 4, pp. 287-308.

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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 
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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/