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

W. Żelazko

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Displaying similar documents to “The strongest vector space topology is locally convex on separable linear subspaces”

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 $m (T)$ .

A non-locally convex topological algebra with all commutative subalgebras locally convex

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].

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.

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...

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.

Local completeness of locally pseudoconvex spaces and Borwein-Preiss variational principle

J. H. Qiu, S. Rolewicz (2007)

Studia Mathematica

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The notion of local completeness is extended to locally pseudoconvex spaces. Then a general version of the Borwein-Preiss variational principle in locally complete locally pseudoconvex spaces is given, where the perturbation is an infinite sum involving differentiable real-valued functions and subadditive functionals. From this, some particular versions of the Borwein-Preiss variational principle are derived. In particular, a version with respect to the Minkowski gauge of a bounded closed...

$ℒ_{p}$ -Spaces and injective locally convex spaces

Paweł Domański

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1985 Mathematics Subject Classification: Primary 46A05, 46A06, 46A12, 46A20, 46A22, 46A99, 46M10, 03C20; Secondary 46E10, 46E15, 46E30, 46C99.

Strict topologies as topological algebras

Surjit Singh Khurana (2001)

Czechoslovak Mathematical Journal

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Let $X$ be a completely regular Hausdorff space, $C_{b} (X)$ the space of all scalar-valued bounded continuous functions on $X$ with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally $m$ -convex.

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.

The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition

Martin Schottenloher (1976)

Annales de l'institut Fourier

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It is proved that the Levi problem for certain locally convex Hausdorff spaces $E$ over $C$ with a finite dimensional Schauder decomposition (for example for Fréchet or Silva spaces with a Schauder basis) the Levi problem has a solution, i.e. every pseudoconvex domain spread over $E$ is a domain of existence of an analytic function. It is also shown that a pseudoconvex domain spread over a Fréchet space or a Silva space with a finite dimensional Schauder decomposition is holomorphically convex...