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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 revised closed graph theorem for quasi-Suslin spaces

Juan Carlos Ferrando, J. Kąkol, M. Lopez Pellicer (2009)

Czechoslovak Mathematical Journal

Some results about the continuity of special linear maps between F -spaces recently obtained by Drewnowski have motivated us to revise a closed graph theorem for quasi-Suslin spaces due to Valdivia. We extend Valdivia’s theorem by showing that a linear map with closed graph from a Baire tvs into a tvs admitting a relatively countably compact resolution is continuous. This also applies to extend a result of De Wilde and Sunyach. A topological space X is said to have a (relatively countably) compact...

Algunos nuevos resultados sobre el teorema de la gráfica cerrada.

Manuel Valdivia (1979)

Revista Matemática Hispanoamericana

Para varios espacios localmente separados, damos aplicaciones lineales no continuas con gráficas cerradas. Uno de los resultados obtenidos contiene el teorema de Mahowald como corolario [7]. Si ε es una clase de espacios localmente convexos separados, estable para límites inductivos y conteniendo los espacios de dimensiones finitas, sea εr la clase de todos los espacios localmente convexos separados tales que si E ∈ ε, F ∈ εr y f es una aplicación lineal de E en F con gráfica cerrada, entonces f...

Baire-like spaces C(X,E)

Jerzy Kakol (2000)

Revista Matemática Complutense

We characterize Baire-like spaces Cc(X,E) of continuous functions defined on a locally compact and Hewitt space X into a locally convex space E endowed with the compact-open topology.

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