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Displaying similar documents to “On functional representation of locally m -pseudoconvex algebras.”

On locally pseudoconvexes square algebras.

Jorma Arhippainen (1995)

Publicacions Matemàtiques

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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.

Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras

M. Abel, J. Arhippainen (2004)

Czechoslovak Mathematical Journal

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Let ( A , T ) be a locally A-pseudoconvex algebra over ℝ or ℂ . We define a new topology m ( T ) on A which is the weakest among all m-pseudoconvex topologies on A stronger than T . We describe a family of non-homogeneous seminorms on A which defines the topology m ( T ) .

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...

A characterization of characters in complex m-pseudoconvex algebras

W. Żelazko (2005)

Banach Center Publications

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In this paper we extend the characterization of characters given in [1], [2] and [8] onto m-pseudoconvex algebras. As a consequence (and a generalization) we give a characterization of continuous homomorphisms from m-pseudoconvex algebras into commutative semisimple m-pseudoconvex algebras.

Topological algebras with maximal regular ideals closed

Mati Abel (2012)

Open Mathematics

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It is shown that all maximal regular ideals in a Hausdorff topological algebra A are closed if the von Neumann bornology of A has a pseudo-basis which consists of idempotent and completant absolutely pseudoconvex sets. Moreover, all ideals in a unital commutative sequentially Mackey complete Hausdorff topological algebra A with jointly continuous multiplication and bounded elements are closed if the von Neumann bornology of A is idempotently pseudoconvex.

On the ideal structure of algebras of LMC-algebra valued functions

Jorma Arhippainen (1992)

Studia Mathematica

Similarity:

Let X be a completely regular topological space and A a commutative locally m-convex algebra. We give a description of all closed and in particular closed maximal ideals of the algebra C(X,A) (= all continuous A-valued functions defined on X). The topology on C(X,A) is defined by a certain family of seminorms. The compact-open topology of C(X,A) is a special case of this topology.