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We study the relation of $L$ -equivalence defined between Tychonoff spaces, that is, we study the topological isomorphisms of their respective free locally convex spaces. We introduce the concept of an $L$ -retract in a Tychonoff space in terms of the existence of a special kind of simultaneous extensions of continuous functions, explore the relation of this concept with the Dugundji extension theorem, and find some conditions that allow us to identify $L$ -retracts in various classes of topological spaces....

Free uniform measures

Jan K. Pachl (1974)

Commentationes Mathematicae Universitatis Carolinae

Gaussian radon measures on locally convex spaces.

Christer Borell (1976)

Mathematica Scandinavica

Gewichtete Räume stetiger vektorwertiger Funktionen und das injektive Tensorprodukt. I.

Klaus-Dieter Bierstedt (1973)

Journal für die reine und angewandte Mathematik

Gewichtete Räume stetiger vektorwertiger Funktionen und das injektive Tensorprodukt. II.

Klaus-Dieter Bierstedt (1973)

Journal für die reine und angewandte Mathematik

Growth Properties of Pseudo-Convex Domains and Domains of Holomorphy in Locally Convex Topological Vector Spaces.

Seán Dineen (1977)

Mathematische Annalen

Hahn-Banach theorem implies Riesz theorem.

Crespin, Daniel (1994)

Portugaliae Mathematica

Hille-Yosida theory in convenient analysis.

Josef Teichmann (2002)

Revista Matemática Complutense

A Hille-Yosida Theorem is proved on convenient vector spaces, a class, which contains all sequentially complete locally convex spaces. The approach is governed by convenient analysis and the credo that many reasonable questions concerning strongly continuous semigroups can be proved on the subspace of smooth vectors. Examples from literature are reconsidered by these simpler methods and some applications to the theory of infinite dimensional heat equations are given.

Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on $ℋ (U)$

Sean Dineen (1973)

Annales de l'institut Fourier

This article is devoted to a study of locally convex topologies on $H (U)$ (where $U$ is an open subset of the locally convex topological vector space $E$ and $H (U)$ is the set of all complex valued holomorphic functions on $E$ ). We discuss the following topologies on $H (U)$ :(a) the compact open topology $I_{0}$ ,(b) the bornological topology associated with $I_{0}$ ,(c) the ported topology of Nachbin $I_{ω}$ ,(d) the bornological topology associated with $I_{ω}$ ; and(e) the $I_{ω}$ topological of Nachbin.For $U$ balanced we show these topologies are...

Holomorphic germs on Banach spaces

Chae Soo Bong (1971)

Annales de l'institut Fourier

Let $E$ and $F$ be two complex Banach spaces, $U$ a nonempty subset of $E$ and $K$ a compact subset of $E$ . The concept of holomorphy type $θ$ between $E$ and $F$ , and the natural locally convex topology $𝒯_{ω, θ}$ on the vector space $ℋ_{θ} (U, F)$ of all holomorphic mappings of a given holomorphy type $θ$ from $U$ to $F$ were considered first by L. Nachbin. Motived by his work, we introduce the locally convex space $ℋ_{θ} (K, F)$ of all germs of holomorphic mappings into $F$ around $K$ of a given holomorphy type $θ$ , and study its interplay with $ℋ_{θ} (U, F)$ and some...

Hyperplanes of Locally Convex Groups

Stojanka Orestijević (1992)

Publications de l'Institut Mathématique

Ideales de riesz en espacios localmente k-convexos

Klaus Madlener (1974)

Revista colombiana de matematicas

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