1,720,976 research outputs found
Extension of polynomials and John's theorem for symmetric tensor products.
Full text linkWe 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
Full text linkWe 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
Diagonal multilinear operators on Köthe sequence spaces
No full textWe 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
Ideals of Multilinear Forms – a Limit Order Approach
Full text linkA general theory of limit orders for ideals of multilinear forms is developed. We relate the limit order of an ideal to those of its maximal hull and its adjoint ideal. We study the limit orders of the ideals of dominated and multiple summing multilinear forms. Finally, estimates of the diagonal of a (non-necessarily diagonal) multilinear form are presented, in terms of the limit order of the ideals to which it belongs.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. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; ArgentinaFil: Sevilla Peris, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Politécnica de Valencia; Españ
Operator p-compact mappings
No full textWe introduce the classes of operator p-compact mappings and completely right p-nuclear operators, which are natural extensions to the operator space framework of their corresponding Banach operator ideals. We relate these two classes, define natural operator space structures and study several properties of these ideals. We show that the class of operator ∞-compact mappings in fact coincides with a notion already introduced by Webster in the nineties (in a very different language). This allows us to provide an operator space structure to Webster's class.Fil: Chávez Domínguez, Javier Alejandro. Oklahoma State University; Estados UnidosFil: Dimant, Veronica Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés; ArgentinaFil: Galicer, Daniel Eric. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin
A fibered description of the vector‐valued spectrum
Full text linkFor Banach spaces X and Y we study the vector-valued spectrum (Formula presented.), that is the set of non null algebra homomorphisms from (Formula presented.) to (Formula presented.), which is naturally projected onto the closed unit ball of (Formula presented.). The aim of this article is to describe the fibers defined by this projection, searching for analytic balls and considering Gleason parts.Fil: Dimant, Veronica Isabel. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Singer, Joaquín Camilo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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
Ideal structures in vector-valued polynomial spaces
Full text linkThis 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
Homomorphisms Between Algebras of Holomorphic Functions on the Infinite Polydisk
No full textWe 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
M-structures in vector-valued polynomial spaces
Full text linkThis 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
No full textWe 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
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