16 research outputs found

    Extension of polynomials and John's theorem for symmetric tensor products.

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    We show that for every infinite-dimensional normed space E and every k ≥ 3 there are extendible k-homogeneous polynomials which are not integral. As a consequence, we prove a symmetric version of a result of John.Fil: Carando, Daniel Germán. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Dimant, Veronica Isabel. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

    Every Banach ideal of polynomials is compatible with an operator ideal

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    We show that for each Banach ideal of homogeneous polynomials, there exists a (necessarily unique) Banach operator ideal compatible with it. Analogously, we prove that any ideal of n-homogeneous polynomials belongs to a coherent sequence of ideals of k-homogeneous polynomials.Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Dimant, Veronica Isabel. Universidad de San Andres; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Muro, Luis Santiago Miguel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

    Biduals of tensor products in operator spaces

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    We study whether the operator space V ∗∗ α ⊗ W∗∗ can be identified with a subspace of the bidual space (V α ⊗ W) ∗∗, for a given operator space tensor norm. We prove that this can be done if α is finitely generated and V and W are locally reflexive. If in addition the dual spaces are locally reflexive and the bidual spaces have the completely bounded approximation property, then the identification is through a complete isomorphism. When α is the projective, Haagerup or injective norm, the hypotheses can be weakened.Fil: Dimant, Veronica Isabel. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Fernández Unzueta, Maite. Centro de Investigación en Matemáticas; Méxic

    M-structures in vector-valued polynomial spaces

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    This paper is concerned with the study of M-structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of weakly continuous on bounded sets n-homogeneous polynomials, Pw(nE; F), is an M-ideal in the space of continuous n-homogeneous polynomials P(nE; F). We show that there is some hope for this to happen only for a finite range of values of n. We establish sufficient conditions under which the problem has positive and negative answers and use the obtained results to study the particular cases when E = lp and F = lq or F is a Lorentz sequence space d(w; q). We extend to our setting the notion of property (M) introduced by Kalton which allows us to lift M-structures from the linear to the vector-valued polynomial context. Also, when Pw(nE; F) is an M-ideal in P(nE; F) we prove a Bishop-Phelps type result for vector-valued polynomials and relate norm-attaining polynomials with farthest points and remotal sets.Fil: Dimant, Veronica Isabel. Universidad de San Andrés; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin

    A look into homomorphisms between uniform algebras over a Hilbert space

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    We study the vector-valued spectrum Mu,∞(Bℓ2,Bℓ2), which is the set of non-zero algebra homomorphisms from Au(Bℓ2) (the algebra of uniformly continuous holomorphic functions on Bℓ2) to H∞(Bℓ2) (the algebra of bounded holomorphic functions on Bℓ2). This set is naturally projected onto the closed unit ball of H∞(Bℓ2,ℓ2) giving rise to an associated fibering. Extending the classical notion of cluster sets introduced by I. J. Schark (1961) to the vector-valued spectrum we define vector-valued cluster sets. The aim of the article is to look at the relationship between fibers and cluster sets obtaining results regarding the existence of analytic balls in those sets.Fil: Dimant, Veronica Isabel. Universidad de San Andrés; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Singer, Joaquín Camilo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires; Argentin

    Diagonal multilinear operators on Köthe sequence spaces

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    We analyse the interplay between maximal/minimal/adjoint ideals of multilinear operators (between sequence spaces) and their associated Köthe sequence spaces. We establish relationships with spaces of multipliers and apply these results to describe diagonal multilinear operators from Lorentz sequence spaces. We also define and study some properties of the ideal of (E, p)-summing multilinear mappings, a natural extension of the linear ideal of absolutely (E, p)-summing operators.Fil: Dimant, Veronica Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés; ArgentinaFil: Villafañe, Norberto Román. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentin

    Homomorphisms Between Algebras of Holomorphic Functions on the Infinite Polydisk

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    We study the vector-valued spectrum M∞(Bc0,Bc0), that is, the set of nonzero algebra homomorphisms from H∞(Bc0) to H∞(Bc0) which is naturally projected onto the closed unit ball of H∞(Bc0,ℓ∞), likewise the scalar-valued spectrum M∞(Bc0) which is projected onto B¯ℓ∞. Our itinerary begins in the scalar-valued spectrum M∞(Bc0): by expanding a result by Cole et al. (Michigan Math J 39(3):551–569, 1992), we prove that in each fiber, there are 2 c disjoint analytic Gleason isometric copies of Bℓ∞. For the vector-valued case, building on the previous result we obtain 2 c disjoint analytic Gleason isometric copies of BH∞(Bc0,ℓ∞) in each fiber. We also take a look at the relationship between fibers and Gleason parts for both vector-valued spectra Mu,∞(Bc0,Bc0) and M∞(Bc0,Bc0).Fil: Dimant, Veronica Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés; ArgentinaFil: Singer, Joaquín Camilo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin

    On the convergence of random polynomials and multilinear forms

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    We consider different kinds of convergence of homogeneous polynomials and multilinear forms in random variables. We show that for a variety of complex random variables, the almost sure convergence of the polynomial is equivalent to that of the multilinear form, and to the square summability of the coefficients. Also, we present polynomial Khintchine inequalities for complex gaussian and Steinhaus variables. All these results have no analogues in the real case. Moreover, we study the Lp-convergence of random polynomials and derive certain decoupling inequalities without the usual tetrahedral hypothesis. We also consider convergence on "full subspaces" in the sense of Sjögren, both for real and complex random variables, and relate it to domination properties of the polynomial or the multilinear form, establishing a link with the theory of homogeneous polynomials on Banach spaces.Fil: Carando, Daniel Germán. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Dimant, Veronica Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; ArgentinaFil: Pinasco, Damian. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad Torcuato Di Tella; Argentin

    Ideal structures in vector-valued polynomial spaces

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    This paper is concerned with the study of geometric structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of n-homogeneous polynomials, Pw(nE,F), which are weakly continuous on bounded sets, is an HB-subspace or an M(1,C)-ideal in the space of continuous n-homogeneous polynomials, P(nE,F). We establish sufficient conditions under which the problem can be positively solved. Some examples are given. We also study when some ideal structures pass from Pw(nE,F) as an ideal in P(nE,F) to the range space F as an ideal in its bidual F∗∗.Fil: Dimant, Veronica Isabel. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; ArgentinaFil: Prieto, Angeles. Universidad Complutense de Madrid; Españ

    The polarization constant of finite dimensional complex spaces is one

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    The polarization constant of a Banach space X is defined as 'Equation Presented' where stands for the best constant C> 0 such that ||Pˇ|| ≤ C||P|| for every k-homogeneous polynomial P ∈ ℘ (kX). We show that if X is a finite dimensional complex space thenc(X)=1. We derive some consequences of this fact regarding the convergence of analytic functions on such spaces. The result is no longer true in the real setting. Here we relate this constant with the so-called Bochnak's complexification procedure. We also study some other properties connected with polarization. Namely, we provide necessary conditions related to the geometry of X for c(2,X)=1 to hold. Additionally we link polarization constants with certain estimates of the nuclear norm of the product of polynomials.Fil: Dimant, Veronica Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; ArgentinaFil: Galicer, Daniel Eric. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rodríguez, Jorge Tomás. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Núcleo Consolidado de Matemática Pura y Aplicada; Argentin
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