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Displaying similar documents to “Locally convex inductive limits of normed algebras”

The Mackey-Arens theorem for non-locally convex spaces.

Jerzy Kakol (1990)

Collectanea Mathematica

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Let R be a subcategory of the category of all topological vector spaces. Let E be an element of R. The problem of the existence of the finest R-topology on E with the same continuous linear functionals as the original one is discussed. Remarks concerning the Hahn-Banach Extension Property are included.

Representation of locally convex algebras.

L. Oubbi (1994)

Revista Matemática de la Universidad Complutense de Madrid

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We deal with the representation of locally convex algebras. On one hand as subalgebras of some weighted space CV(X) and on the other hand, in the case of uniformly A-convex algebras, as inductive limits of Banach algebras. We also study some questions on the spectrum of a locally convex algebra.

On vector spaces and algebras with maximal locally pseudoconvex topologies

A. Kokk, W. Żelazko (1995)

Studia Mathematica

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Let X be a real or complex vector space. We show that the maximal p-convex topology makes X a complete Hausdorff topological vector space. If X has an uncountable dimension, then different p give different topologies. However, if the dimension of X is at most countable, then all these topologies coincide. This leads to an example of a complete locally pseudoconvex space X that is not locally convex, but all of whose separable subspaces are locally convex. We apply these results to topological...