Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras

M. Abel; J. Arhippainen

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Displaying similar documents to “Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras”

The strongest vector space topology is locally convex on separable linear subspaces

W. Żelazko (1997)

Annales Polonici Mathematici

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Let X be a real or complex vector space equipped with the strongest vector space topology $τ_{m a x}$ . Besides the result announced in the title we prove that X is uncountable-dimensional if and only if it is not locally pseudoconvex.

Topological algebras with pseudoconvexly bounded elements

Mati Abel (2005)

Banach Center Publications

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It is shown that every commutative sequentially bornologically complete Hausdorff algebra A with bounded elements is representable in the form of an (algebraic) inductive limit of an inductive system of locally bounded Fréchet algebras with continuous monomorphisms if the von Neumann bornology of A is pseudoconvex. Several classes of topological algebras A for which $r_{A} (a) \leq β_{A} (a)$ or $r_{A} (a) = β_{A} (a)$ for each a ∈ A are described.

A note on quasiconvex functions that are pseudoconvex.

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.

On functional representation of locally $m$ -pseudoconvex algebras.

Arhippainen, Jorma (1999)

International Journal of Mathematics and Mathematical Sciences

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Real Gel'fand-Mazur division algebras.

Abel, Mati, Panova, Olga (2003)

International Journal of Mathematics and Mathematical Sciences

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Real Gelfand-Mazur algebras.

Panova, Olga (2006)

Portugaliae Mathematica. Nova Série

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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.

Diametral dimension of some pseudoconvex multiscale spaces

Jean-Marie Aubry, Françoise Bastin (2010)

Studia Mathematica

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Stemming from the study of signals via wavelet coefficients, the spaces $S^{ν}$ are complete metrizable and separable topological vector spaces, parametrized by a function ν, whose elements are sequences indexed by a binary tree. Several papers were devoted to their basic topology; recently it was also shown that depending on ν, $S^{ν}$ may be locally convex, locally p-convex for some p > 0, or not at all, but under a minor condition these spaces are always pseudoconvex. We deal with some more...

A remark on semiglobal existence for $\bar{\partial}$

Alberto Scalari (1997)

Rendiconti del Seminario Matematico della Università di Padova

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The pluricomplex Green function on some regular pseudoconvex domains

Gregor Herbort (2014)

Annales Polonici Mathematici

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Let D be a smooth bounded pseudoconvex domain in ℂⁿ of finite type. We prove an estimate on the pluricomplex Green function $_{D} (z, w)$ of D that gives quantitative information on how fast the Green function vanishes if the pole w approaches the boundary. Also the Hölder continuity of the Green function is discussed.

A smooth Pseudoconvex domain without pseudoconvex exhaustion.

Klas Diederich, John Erik Fornaess (1982)

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Peak functions on convex domains

Kolář, Martin

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Let $Ω \subset ℂ^{n}$ be a domain with smooth boundary and $p \in \partial Ω$ . A holomorphic function $f$ on $Ω$ is called a $C^{k}$ ( $k = 0, 1, 2, \dots$ ) peak function at $p$ if $f \in C^{k} (\bar{Ω})$ , $f (p) = 1$ , and $| f (q) | < 1$ for all $q \in \bar{Ω} ∖ {p}$ . If $Ω$ is strongly pseudoconvex, then $C^{\infty}$ peak functions exist. On the other hand, J. E. Fornaess constructed an example in $ℂ^{2}$ to show that this result fails, even for $C^{1}$ functions, on a weakly pseudoconvex domain [Math. Ann. 227, 173-175 (1977; Zbl 0346.32026)]. Subsequently, E. Bedford and J. E. Fornaess showed that there is always a continuous peak function...