Atomic decompositions for tensor products and polynomial spaces
We study the existence of atomic decompositions for tensor products of Banach spaces and spaces of homogeneous polynomials. If a Banach space X admits an atomic decomposition of a certain kind, we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic...
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2008
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p243_Carando https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v347_n1_p243_Carando_oai |
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I28-R145-paper_0022247X_v347_n1_p243_Carando_oai2024-08-16 Carando, D. Lassalle, S. 2008 We study the existence of atomic decompositions for tensor products of Banach spaces and spaces of homogeneous polynomials. If a Banach space X admits an atomic decomposition of a certain kind, we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic decomposition for the symmetric tensor product ⊗s, μ n X, for any symmetric tensor norm μ. In addition, the reciprocal statement is investigated and analogous consequences for the full tensor product are obtained. Finally we apply the previous results to establish the existence of monomial atomic decompositions for certain ideals of polynomials on X. © 2008 Elsevier Inc. All rights reserved. Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Lassalle, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p243_Carando info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Math. Anal. Appl. 2008;347(1):243-254 Atomic decompositions Homogeneous polynomials Polynomial ideals Symmetric tensor norms Tensor products Atomic decompositions for tensor products and polynomial spaces info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v347_n1_p243_Carando_oai |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-145 |
| collection |
Repositorio Digital de la Universidad de Buenos Aires (UBA) |
| topic |
Atomic decompositions Homogeneous polynomials Polynomial ideals Symmetric tensor norms Tensor products |
| spellingShingle |
Atomic decompositions Homogeneous polynomials Polynomial ideals Symmetric tensor norms Tensor products Carando, D. Lassalle, S. Atomic decompositions for tensor products and polynomial spaces |
| topic_facet |
Atomic decompositions Homogeneous polynomials Polynomial ideals Symmetric tensor norms Tensor products |
| description |
We study the existence of atomic decompositions for tensor products of Banach spaces and spaces of homogeneous polynomials. If a Banach space X admits an atomic decomposition of a certain kind, we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic decomposition for the symmetric tensor product ⊗s, μ n X, for any symmetric tensor norm μ. In addition, the reciprocal statement is investigated and analogous consequences for the full tensor product are obtained. Finally we apply the previous results to establish the existence of monomial atomic decompositions for certain ideals of polynomials on X. © 2008 Elsevier Inc. All rights reserved. |
| format |
Artículo Artículo publishedVersion |
| author |
Carando, D. Lassalle, S. |
| author_facet |
Carando, D. Lassalle, S. |
| author_sort |
Carando, D. |
| title |
Atomic decompositions for tensor products and polynomial spaces |
| title_short |
Atomic decompositions for tensor products and polynomial spaces |
| title_full |
Atomic decompositions for tensor products and polynomial spaces |
| title_fullStr |
Atomic decompositions for tensor products and polynomial spaces |
| title_full_unstemmed |
Atomic decompositions for tensor products and polynomial spaces |
| title_sort |
atomic decompositions for tensor products and polynomial spaces |
| publishDate |
2008 |
| url |
http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p243_Carando https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v347_n1_p243_Carando_oai |
| work_keys_str_mv |
AT carandod atomicdecompositionsfortensorproductsandpolynomialspaces AT lassalles atomicdecompositionsfortensorproductsandpolynomialspaces |
| _version_ |
1809357072226058240 |