Sequentially m-barrelled algebras.

Siham Jalal Al-Sayyad

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*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,...