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Abstract:

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.

Registro:

Documento: Artículo
Título:The ideal of p-compact operators: A tensor product approach
Autor:Galicer, D.; Lassalle, S.; Turco, P.
Filiación:Departamento de Matematica - Pab. I, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
Palabras clave:Absolutely p-summing operators; Approximation properties; P-compact operators; Quasi p-nuclear operators; Tensor norms
Año:2012
Volumen:211
Número:3
Página de inicio:269
Página de fin:286
DOI: http://dx.doi.org/10.4064/sm211-3-8
Título revista:Studia Mathematica
Título revista abreviado:Stud. Math.
ISSN:00393223
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v211_n3_p269_Galicer

Referencias:

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Citas:

---------- APA ----------
Galicer, D., Lassalle, S. & Turco, P. (2012) . The ideal of p-compact operators: A tensor product approach. Studia Mathematica, 211(3), 269-286.
http://dx.doi.org/10.4064/sm211-3-8
---------- CHICAGO ----------
Galicer, D., Lassalle, S., Turco, P. "The ideal of p-compact operators: A tensor product approach" . Studia Mathematica 211, no. 3 (2012) : 269-286.
http://dx.doi.org/10.4064/sm211-3-8
---------- MLA ----------
Galicer, D., Lassalle, S., Turco, P. "The ideal of p-compact operators: A tensor product approach" . Studia Mathematica, vol. 211, no. 3, 2012, pp. 269-286.
http://dx.doi.org/10.4064/sm211-3-8
---------- VANCOUVER ----------
Galicer, D., Lassalle, S., Turco, P. The ideal of p-compact operators: A tensor product approach. Stud. Math. 2012;211(3):269-286.
http://dx.doi.org/10.4064/sm211-3-8