Approximation properties determined by operator ideals and approximability of homogeneous polynomials and holomorphic functions

Sonia Berrios; Geraldo Botelho

Displaying similar documents to “Approximation properties determined by operator ideals and approximability of homogeneous polynomials and holomorphic functions”

Integral holomorphic functions

Verónica Dimant, Pablo Galindo, Manuel Maestre, Ignacio Zalduendo (2004)

Studia Mathematica

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We define the class of integral holomorphic functions over Banach spaces; these are functions admitting an integral representation akin to the Cauchy integral formula, and are related to integral polynomials. After studying various properties of these functions, Banach and Fréchet spaces of integral holomorphic functions are defined, and several aspects investigated: duality, Taylor series approximation, biduality and reflexivity.

Infinite-factorable holomorphic mappings on locally convex spaces.

Ralf Hollstein (1986)

Collectanea Mathematica

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Holomorphic Approximation of Ultradifferentiable Functions.

Bernd Droste (1981)

Mathematische Annalen

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Surjective factorization of holomorphic mappings

Manuel Gonzalez, Joaquín M. Gutiérrez (2000)

Commentationes Mathematicae Universitatis Carolinae

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We characterize the holomorphic mappings $f$ between complex Banach spaces that may be written in the form $f = T \circ g$ , where $g$ is another holomorphic mapping and $T$ belongs to a closed surjective operator ideal.

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Joaquim Bruna, Josep Ma. Burgues (1984)

Mathematische Annalen

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Lineability and algebrability of the set of holomorphic functions with a given domain of existence

Thiago R. Alves (2014)

Studia Mathematica

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We show that if U is a domain of existence in a separable Banach space, then the set of holomorphic functions on U whose domain of existence is U is lineable and algebrable.

Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces

Erhan Çalışkan (2007)

Czechoslovak Mathematical Journal

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We show that a Banach space $E$ has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on $E$ can be uniformly approximated on compact sets by homogeneous polynomials which are members of the ideal of homogeneous polynomials generated by weakly compact linear operators. An analogous result is established also for the compact approximation property.

Some aspects of holomorphic approximations from the point of view of PDEs

Roman Dwilewicz, Paul M. Gauthier (1987)

Banach Center Publications

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Fixed points of holomorphic mappings for domains in Banach spaces.

Harris, Lawrence A. (2003)

Abstract and Applied Analysis

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Bounded holomorphic mappings and the compact approximation property in Banach spaces.

Çalişkan, Erhan (2004)

Portugaliae Mathematica. Nova Série

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The bounded approximation property for the predual of the space of bounded holomorphic mappings

Erhan Çalışkan (2006)

Studia Mathematica

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When U is the open unit ball of a separable Banach space E, we show that $G^{\infty} (U)$ , the predual of the space of bounded holomorphic mappings on U, has the bounded approximation property if and only if E has the bounded approximation property.

On bounded approximation properties of Banach spaces

Eve Oja (2010)

Banach Center Publications

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This survey features some recent developments concerning the bounded approximation property in Banach spaces. As a central theme, we discuss the weak bounded approximation property and the approximation property which is bounded for a Banach operator ideal. We also include an overview around the related long-standing open problem: Is the approximation property of a dual Banach space always metric?