Asymptotic estimates on the von Neumann inequality for homogeneous polynomials

By the von Neumann inequality for homogeneous polynomials there exists a positive constant Ck,q(n) such that for every k-homogeneous polynomial p in n variables and every n-tuple of commuting operators (T1.... Tn) with ∑n i=1 Tiq ≤ 1 [EQUATION PRESENTED] we have For fixed k and q, we study the asymp...

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Publicado: 2018
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00754102_v2018_n743_p213_Galicer
http://hdl.handle.net/20.500.12110/paper_00754102_v2018_n743_p213_Galicer
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00754102_v2018_n743_p213_Galicer
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spelling paper:paper_00754102_v2018_n743_p213_Galicer2023-06-08T15:07:07Z Asymptotic estimates on the von Neumann inequality for homogeneous polynomials By the von Neumann inequality for homogeneous polynomials there exists a positive constant Ck,q(n) such that for every k-homogeneous polynomial p in n variables and every n-tuple of commuting operators (T1.... Tn) with ∑n i=1 Tiq ≤ 1 [EQUATION PRESENTED] we have For fixed k and q, we study the asymptotic growth of the smallest constant Ck,qn as n (the number of variables/operators) tends to infinity. For q = ∞, we obtain the correct asymptotic behavior of this constant (answering a question posed by Dixon in the 1970s). For 2 ≤ q < ∞ we improve some lower bounds given by Mantero and Tonge, and prove the asymptotic behavior up to a logarithmic factor. To achieve this we provide estimates of the norm of homogeneous unimodular Steiner polynomials, i.e. polynomials such that the multi-indices corresponding to the nonzero coefficients form partial Steiner systems. © 2018 De Gruyter. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00754102_v2018_n743_p213_Galicer http://hdl.handle.net/20.500.12110/paper_00754102_v2018_n743_p213_Galicer
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description By the von Neumann inequality for homogeneous polynomials there exists a positive constant Ck,q(n) such that for every k-homogeneous polynomial p in n variables and every n-tuple of commuting operators (T1.... Tn) with ∑n i=1 Tiq ≤ 1 [EQUATION PRESENTED] we have For fixed k and q, we study the asymptotic growth of the smallest constant Ck,qn as n (the number of variables/operators) tends to infinity. For q = ∞, we obtain the correct asymptotic behavior of this constant (answering a question posed by Dixon in the 1970s). For 2 ≤ q < ∞ we improve some lower bounds given by Mantero and Tonge, and prove the asymptotic behavior up to a logarithmic factor. To achieve this we provide estimates of the norm of homogeneous unimodular Steiner polynomials, i.e. polynomials such that the multi-indices corresponding to the nonzero coefficients form partial Steiner systems. © 2018 De Gruyter.
title Asymptotic estimates on the von Neumann inequality for homogeneous polynomials
spellingShingle Asymptotic estimates on the von Neumann inequality for homogeneous polynomials
title_short Asymptotic estimates on the von Neumann inequality for homogeneous polynomials
title_full Asymptotic estimates on the von Neumann inequality for homogeneous polynomials
title_fullStr Asymptotic estimates on the von Neumann inequality for homogeneous polynomials
title_full_unstemmed Asymptotic estimates on the von Neumann inequality for homogeneous polynomials
title_sort asymptotic estimates on the von neumann inequality for homogeneous polynomials
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00754102_v2018_n743_p213_Galicer
http://hdl.handle.net/20.500.12110/paper_00754102_v2018_n743_p213_Galicer
_version_ 1768541601617936384

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