Real Gel'fand-Mazur division algebras.
Abel, Mati, Panova, Olga (2003)
International Journal of Mathematics and Mathematical Sciences
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Abel, Mati, Panova, Olga (2003)
International Journal of Mathematics and Mathematical Sciences
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Abel, Mart, Abel, Mati (2006)
International Journal of Mathematics and Mathematical Sciences
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Arhippainen, Jorma (1999)
International Journal of Mathematics and Mathematical Sciences
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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.
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.
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.
M. Abel, J. Arhippainen (2004)
Czechoslovak Mathematical Journal
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Let be a locally A-pseudoconvex algebra over or . We define a new topology on which is the weakest among all m-pseudoconvex topologies on stronger than . We describe a family of non-homogeneous seminorms on which defines the topology .
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...
W. Żelazko (1996)
Studia Mathematica
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We construct a complete multiplicatively pseudoconvex algebra with the property announced in the title. This solves Problem 25 of [6].
Mati Abel, Krzysztof Jarosz (2005)
Banach Center Publications
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We characterize unital topological algebras in which all maximal two-sided ideals are closed.
Giorgio Giorgi (1987)
Trabajos de Investigación Operativa
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In the present note we consider the definitions and properties of locally pseudo- and quasiconvex functions and give a sufficient condition for a locally quasiconvex function at a point x ∈ R, to be also locally pseudoconvex at the same point.