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A class of locally convex spaces without 𝒞 -webs

Manuel Valdivia (1982)

Annales de l'institut Fourier

In this article we give some properties of the tensor product, with the ϵ and π topologies, of two locally convex spaces. As a consequence we prove that the theory of M. de Wilde of the closed graph theorem does not contain the closed graph theorem of L. Schwartz.

A class of statistical and σ -conservative matrices

Hüsamettin Çoşkun, Celal Çakan (2005)

Czechoslovak Mathematical Journal

In [5] and [10], statistical-conservative and σ -conservative matrices were characterized. In this note we have determined a class of statistical and σ -conservative matrices studying some inequalities which are analogous to Knopp’s Core Theorem.

A converse to Amir-Lindenstrauss theorem in complex Banach spaces.

Ondrej F. K. Kalenda (2006)

RACSAM

We show that a complex Banach space is weakly Lindelöf determined if and only if the dual unit ball of any equivalent norm is weak* Valdivia compactum. We deduce that a complex Banach space X is weakly Lindelöf determined if and only if any nonseparable Banach space isomorphic to a complemented subspace of X admits a projectional resolution of the identity. These results complete the previous ones on real spaces.

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