Displaying similar documents to “A non-locally convex topological algebra with all commutative subalgebras locally convex”

On vector spaces and algebras with maximal locally pseudoconvex topologies

A. Kokk, W. Żelazko (1995)

Studia Mathematica

Similarity:

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...

On locally pseudoconvexes square algebras.

Jorma Arhippainen (1995)

Publicacions Matemàtiques

Similarity:

Let A be an algebra over the field of complex numbers with a (Hausdorff) topology given by a family Q = {q|λ ∈ Λ} of square preserving r-homogeneous seminorms (r ∈ (0, 1]). We shall show that (A, T(Q)) is a locally m-convex algebra. Furthermore we shall show that A is commutative.

The three-space-problem for locally-m-convex algebras.

Susanne Dierolf, Thomas Heintz (2003)

RACSAM

Similarity:

We prove that a locally convex algebra A with jointly continuous multiplication is already locally-m-convex, if A contains a two-sided ideal I such that both I and the quotient algebra A/I are locally-m-convex. An application to the behaviour of the associated locally-m-convex topology on ideals is given.

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

Jerzy Kakol (1990)

Collectanea Mathematica

Similarity:

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.