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...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00754102_v2018_n743_p213_Galicer |
| Aporte de: |
| id |
todo:paper_00754102_v2018_n743_p213_Galicer |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_00754102_v2018_n743_p213_Galicer2023-10-03T14:53:56Z Asymptotic estimates on the von Neumann inequality for homogeneous polynomials Galicer, D. Muro, S. Sevilla-Peris, P. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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. |
| format |
JOUR |
| author |
Galicer, D. Muro, S. Sevilla-Peris, P. |
| spellingShingle |
Galicer, D. Muro, S. Sevilla-Peris, P. Asymptotic estimates on the von Neumann inequality for homogeneous polynomials |
| author_facet |
Galicer, D. Muro, S. Sevilla-Peris, P. |
| author_sort |
Galicer, D. |
| title |
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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00754102_v2018_n743_p213_Galicer |
| work_keys_str_mv |
AT galicerd asymptoticestimatesonthevonneumanninequalityforhomogeneouspolynomials AT muros asymptoticestimatesonthevonneumanninequalityforhomogeneouspolynomials AT sevillaperisp asymptoticestimatesonthevonneumanninequalityforhomogeneouspolynomials |
| _version_ |
1782030131350470656 |