Domingo Garcia - Academia.edu (original) (raw)

Papers by Domingo Garcia

Journal of Functional Analysis, 2006

We show that the set of N -linear mappings on a product of N Banach spaces such that all their Ar... more We show that the set of N -linear mappings on a product of N Banach spaces such that all their Arens extensions attain their norms (at the same element) is norm dense in the space of all bounded N -linear mappings.

Journal of Mathematical Analysis and Applications, 2004

Let C(K, C) be the Banach space of all complex-valued continuous functions on a compact Hausdorff... more Let C(K, C) be the Banach space of all complex-valued continuous functions on a compact Hausdorff space K. We study when the following statement holds: every norm attaining n-homogeneous complex polynomial on C(K, C) attains its norm at extreme points. We prove that this property is true whenever K is a compact Hausdorff space of dimension less than or equal to one. In the case of a compact metric space a characterization is obtained. As a consequence we show that, for a scattered compact Hausdorff space K, every continuous n-homogeneous complex polynomial on C(K, C) can be approximated by norm attaining ones at extreme points and also that the set of all extreme points of the unit ball of C(K, C) is a norming set for every continuous complex polynomial. Similar results can be obtained if "norm" is replaced by "numerical radius."

Journal of Functional Analysis, 2008

We prove the Bishop-Phelps-Bollobás theorem for operators from an arbitrary Banach space X into a... more We prove the Bishop-Phelps-Bollobás theorem for operators from an arbitrary Banach space X into a Banach space Y whenever the range space has property β of Lindenstrauss. We also characterize those Banach spaces Y for which the Bishop-Phelps-Bollobás theorem holds for operators from 1 into Y . Several examples of classes of such spaces are provided. For instance, the Bishop-Phelps-Bollobás theorem holds when the range space is finite-dimensional, an L 1 (μ)-space for a σ -finite measure μ, a C(K)-space for a compact Hausdorff space K, or a uniformly convex Banach space. (R.M. Aron), domingo.garcia@uv.es (D. García), manuel.maestre@uv.es (M. Maestre).

Mathematische Annalen, 2008

Bohr showed that the width of the strip (in the complex plane) on which a given Dirichlet series ... more Bohr showed that the width of the strip (in the complex plane) on which a given Dirichlet series suman/ns,,sinmathbbC{\sum a_n/ n^s, \, s \in \mathbb{C}}suman/ns,,sinmathbbC , converges uniformly but not absolutely, is at most 1/2, and Bohnenblust-Hille that this bound in general is optimal. We prove that for a given infinite dimensional Banach space Y the width of Bohr’s strip for a Dirichlet series with coefficients a n in Y is bounded by 1 - 1/Cot (Y), where Cot (Y) denotes the optimal cotype of Y. This estimate even turns out to be optimal, and hence leads to a new characterization of cotype in terms of vector valued Dirichlet series.

Studia Mathematica, 2007

2000 Mathematics Subject Classification: Primary 46G25; Secondary 46B20, 47A12. Key words and phr... more 2000 Mathematics Subject Classification: Primary 46G25; Secondary 46B20, 47A12. Key words and phrases: polynomial, Banach space, Daugavet equation, numerical range. The first author was supported by grant No. R01-2004-000-10055-0 from the Basic Research Program of ...

Journal of Mathematical Analysis and Applications, 1992

Advances in Mathematics, 2005

Let U and V be convex and balanced open subsets of the Banach spaces X and Y respectively. In thi... more Let U and V be convex and balanced open subsets of the Banach spaces X and Y respectively. In this paper we study the following question: Given two Fréchet algebras of holomorphic functions of bounded type on U and V respectively that are algebra-isomorphic, can we deduce that X and Y (or X * and Y * ) are isomorphic? We prove that if X * or Y * has the approximation property and H wu (U ) and H wu (V ) are topologically algebra-isomorphic, then X * and Y * are isomorphic (the converse being true when U and V are the whole space). We get analogous results for H b (U ) and H b (V ), giving conditions under which an algebra-isomorphism between H b (X) and H b (Y ) is equivalent to an isomorphism between X * and Y * . We also obtain characterizations of different algebra-homomorphisms as composition operators, study the structure of the spectrum of the algebras under consideration and show the existence of homomorphisms on H b (X) with pathological behaviors. 22 and 23. Since T * is reflexive, if U ⊂ T * and V ⊂ Y are convex and balanced open sets and H b (U ) and H b (V ) are topologically algebra-isomorphic, then T * and Y are isomorphic. Moreover, H b (T * ) and H b (Y ) are isomorphic if and only if T * and Y are isomorphic.

Mathematische Nachrichten, 2010

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions... more The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on ℝn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Journal of Approximation Theory, 2004

We obtain general lower and upper estimates for the first and the second Bohr radii of bounded co... more We obtain general lower and upper estimates for the first and the second Bohr radii of bounded complete Reinhardt domains in C n : r 2004 Elsevier Inc. All rights reserved.

Journal Fur Die Reine Und Angewandte Mathematik, 2003

Page 1. J. reine angew. Math. 557 (2003), 173197 Journal für die reine und angewandte Mathematik... more Page 1. J. reine angew. Math. 557 (2003), 173197 Journal für die reine und angewandte Mathematik ( Walter de Gruyter Berlin Á New York 2003 Bohr's power series theorem and local Banach space theory To the memory of our friend Klaus Floret ...

Proceedings of The Edinburgh Mathematical Society, 2006

... (vi) The inequality n(k)(E ∗∗ ) ⩽ n(k)(E) for every Banach space E. In § 3 some results about... more ... (vi) The inequality n(k)(E ∗∗ ) ⩽ n(k)(E) for every Banach space E. In § 3 some results about the numerical radius of multilinear maps and homogeneous polynomials on C(K) and the disc algebra are given. 2. Properties of the polynomial numerical index of order k ...

Mathematische Nachrichten, 1993

We show that holomorphic mappings of bounded type defined on Fréchet spaces extend to the bidual.... more We show that holomorphic mappings of bounded type defined on Fréchet spaces extend to the bidual. The relationship between holomorphic mappings of bounded type and of uniformly bounded type is discussed and some algebraic and topological properties of the space of all entire mappings of (uniformly) bounded type are proved, for example a holomorphic version of Schauder's theorem.

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