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.
