The ideal of p-compact operators: A tensor product approach

We study the space of p-compact operators, Kp, using the theory of tensor norms and operator ideals. We prove that Kp is associated to /dp, the left injective associate of the Chevet-Saphar tensor norm dp (which is equal to g' p' ). This allows us to relate the theory of p-summing operator...

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Detalles Bibliográficos
Autores principales:	Galicer, Daniel Eric, Lassalle, Silvia Beatriz
Publicado:	2012
Materias:	Absolutely p-summing operators Approximation properties P-compact operators Quasi p-nuclear operators Tensor norms
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v211_n3_p269_Galicer http://hdl.handle.net/20.500.12110/paper_00393223_v211_n3_p269_Galicer
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_00393223_v211_n3_p269_Galicer
record_format	dspace
spelling	paper:paper_00393223_v211_n3_p269_Galicer2023-06-08T15:03:33Z The ideal of p-compact operators: A tensor product approach Galicer, Daniel Eric Lassalle, Silvia Beatriz Absolutely p-summing operators Approximation properties P-compact operators Quasi p-nuclear operators Tensor norms We study the space of p-compact operators, Kp, using the theory of tensor norms and operator ideals. We prove that Kp is associated to /dp, the left injective associate of the Chevet-Saphar tensor norm dp (which is equal to g' p' ). This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that K p(E; F) is equal to Kq(E; F) for a wide range of values of p and q, and show that our results are sharp. We also exhibit several structural properties of Kp. For instance, we show that Kp is regular, surjective, and totally accessible, and we characterize its maximal hull Kmax p as the dual ideal of p-summing operators, Πdual p . Furthermore, we prove that Kp coincides isometrically with QNdual p , the dual to the ideal of the quasi p-nuclear operators. © Instytut Matematyczny PAN, 2012. Fil:Galicer, 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. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v211_n3_p269_Galicer http://hdl.handle.net/20.500.12110/paper_00393223_v211_n3_p269_Galicer
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Absolutely p-summing operators Approximation properties P-compact operators Quasi p-nuclear operators Tensor norms
spellingShingle	Absolutely p-summing operators Approximation properties P-compact operators Quasi p-nuclear operators Tensor norms Galicer, Daniel Eric Lassalle, Silvia Beatriz The ideal of p-compact operators: A tensor product approach
topic_facet	Absolutely p-summing operators Approximation properties P-compact operators Quasi p-nuclear operators Tensor norms
description	We study the space of p-compact operators, Kp, using the theory of tensor norms and operator ideals. We prove that Kp is associated to /dp, the left injective associate of the Chevet-Saphar tensor norm dp (which is equal to g' p' ). This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that K p(E; F) is equal to Kq(E; F) for a wide range of values of p and q, and show that our results are sharp. We also exhibit several structural properties of Kp. For instance, we show that Kp is regular, surjective, and totally accessible, and we characterize its maximal hull Kmax p as the dual ideal of p-summing operators, Πdual p . Furthermore, we prove that Kp coincides isometrically with QNdual p , the dual to the ideal of the quasi p-nuclear operators. © Instytut Matematyczny PAN, 2012.
author	Galicer, Daniel Eric Lassalle, Silvia Beatriz
author_facet	Galicer, Daniel Eric Lassalle, Silvia Beatriz
author_sort	Galicer, Daniel Eric
title	The ideal of p-compact operators: A tensor product approach
title_short	The ideal of p-compact operators: A tensor product approach
title_full	The ideal of p-compact operators: A tensor product approach
title_fullStr	The ideal of p-compact operators: A tensor product approach
title_full_unstemmed	The ideal of p-compact operators: A tensor product approach
title_sort	ideal of p-compact operators: a tensor product approach
publishDate	2012
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v211_n3_p269_Galicer http://hdl.handle.net/20.500.12110/paper_00393223_v211_n3_p269_Galicer
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The ideal of p-compact operators: A tensor product approach

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