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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todo:paper_00393223_v211_n3_p269_Galicer2023-10-03T14:49:47Z The ideal of p-compact operators: A tensor product approach Galicer, D. Lassalle, S. Turco, P. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, D. Lassalle, S. Turco, P. 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. |
| format |
JOUR |
| author |
Galicer, D. Lassalle, S. Turco, P. |
| author_facet |
Galicer, D. Lassalle, S. Turco, P. |
| author_sort |
Galicer, D. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00393223_v211_n3_p269_Galicer |
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