Displaying similar documents to “A note on spaces of holomorphic vector valued functions with the strict topology.”

Factorization of weakly continuous holomorphic mappings

Manuel González, Joaqín Gutiérrez (1996)

Studia Mathematica

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We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly uniformly} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced...

On sequential convergence in weakly compact subsets of Banach spaces

Witold Marciszewski (1995)

Studia Mathematica

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We construct an example of a Banach space E such that every weakly compact subset of E is bisequential and E contains a weakly compact subset which cannot be embedded in a Hilbert space equipped with the weak topology. This answers a question of Nyikos.