Holomorphic germs on Banach spaces

Chae Soo Bong

Displaying similar documents to “Holomorphic germs on Banach spaces”

Approximation of holomorphic functions in Banach spaces admitting a Schauder decomposition

Francine Meylan (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let $X$ be a complex Banach space. Recall that $X$ admits aif there exists a sequence ${X_{n}}_{n = 1}^{\infty}$ of finite-dimensional subspaces of $X,$ such that every $x \in X$ has a unique representation of the form $x = \sum_{n = 1}^{\infty} x_{n},$ with $x_{n} \in X_{n}$ for every $n .$ The finite-dimensional Schauder decomposition is said to beif, for every $x \in X,$ the series $x = \sum_{n = 1}^{\infty} x_{n},$ which represents $x,$ converges unconditionally, that is, $\sum_{n = 1}^{\infty} x_{π (n)}$ converges for every permutation $π$ of the integers. For short, we say that $X$ admits an unconditional F.D.D.We show that if X admits an unconditional...

A special version of the Schwarz lemma on an infinite dimensional domain

Tatsuhiro Honda (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $B$ be the open unit ball of a Banach space $E$ , and let $f : B \to B$ be a holomorphic map with $f (0) = 0$ . In this paper, we discuss a condition whereby $f$ is a linear isometry on $E$ .

On the Rogosinski radius for holomorphic mappings and some of its applications

Lev Aizenberg, Mark Elin, David Shoikhet (2005)

Studia Mathematica

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The well known theorem of Rogosinski asserts that if the modulus of the sum of a power series is less than 1 in the open unit disk: $| \sum_{n = 0}^{\infty} a ₙ z ⁿ | < 1$ , |z| < 1, then all its partial sums are less than 1 in the disk of radius 1/2: $| \sum_{n = 0}^{k} a ₙ z ⁿ | < 1$ , |z| < 1/2, and this radius is sharp. We present a generalization of this theorem to holomorphic mappings of the open unit ball into an arbitrary convex domain. Other multidimensional analogs of Rogosinski’s theorem as well as some applications to dynamical systems are...

Simple construction of spaces without the Hahn-Banach extension property

Jerzy Kąkol (1992)

Commentationes Mathematicae Universitatis Carolinae

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An elementary construction for an abundance of vector topologies $ξ$ on a fixed infinite dimensional vector space $E$ such that $(E, ξ)$ has not the Hahn-Banach extension property but the topological dual ${(E, ξ)}^{'}$ separates points of $E$ from zero is given.

Some characterizations of ultrabornological spaces

Manuel Valdivia (1974)

Annales de l'institut Fourier

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Let $U$ be an infinite-dimensional separable Fréchet space with a topology defined by a family of norms. Let $F$ be an infinite-dimensional Banach space. Then $F$ is the inductive limit of a family of spaces equal to $E$ . The choice of suitable classes of Fréchet spaces allows to give characterizations of ultrabornological spaces using the result above.. Let $Ω$ be a non-empty open set in the euclidean $n$ -dimensional space $R^{n}$ . Then $F$ is the inductive limit of a family of spaces equal to $D (Ω)$ . ...