Abstract:
We use the notion of A-compact sets (determined by an operator ideal A), introduced by Carl and Stephani (1984), to show that many known results of certain approximation properties and several ideals of compact operators can be systematically studied under this framework. For Banach operator ideals A, we introduce a way to measure the size of A-compact sets and use it to give a norm on KA, the ideal of A-compact operators. Then, we study two types of approximation properties determined by A-compact sets. We focus our attention on an approximation property which makes use of the norm defined on KA. This notion fits the definition of the A-approximation property, recently introduced by Oja (2012), with KA instead of A. We exemplify the power of the Carl-Stephani theory and the geometric structure introduced here by appealing to some recent developments on p-compactness. © 2013 Elsevier Inc.
Registro:
Documento: |
Artículo
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Título: | The Banach ideal of A-compact operators and related approximation properties |
Autor: | Lassalle, S.; Turco, P. |
Filiación: | Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, B1644BID, Victoria, Buenos Aires, Argentina IMAS - CONICET, Argentina Departamento de Matemática - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, 1428, Buenos Aires, Argentina
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Palabras clave: | Approximation properties; Compact sets; Operator ideals |
Año: | 2013
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Volumen: | 265
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Número: | 10
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Página de inicio: | 2452
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Página de fin: | 2464
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DOI: |
http://dx.doi.org/10.1016/j.jfa.2013.07.001 |
Título revista: | Journal of Functional Analysis
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Título revista abreviado: | J. Funct. Anal.
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ISSN: | 00221236
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CODEN: | JFUAA
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v265_n10_p2452_Lassalle |
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Citas:
---------- APA ----------
Lassalle, S. & Turco, P.
(2013)
. The Banach ideal of A-compact operators and related approximation properties. Journal of Functional Analysis, 265(10), 2452-2464.
http://dx.doi.org/10.1016/j.jfa.2013.07.001---------- CHICAGO ----------
Lassalle, S., Turco, P.
"The Banach ideal of A-compact operators and related approximation properties"
. Journal of Functional Analysis 265, no. 10
(2013) : 2452-2464.
http://dx.doi.org/10.1016/j.jfa.2013.07.001---------- MLA ----------
Lassalle, S., Turco, P.
"The Banach ideal of A-compact operators and related approximation properties"
. Journal of Functional Analysis, vol. 265, no. 10, 2013, pp. 2452-2464.
http://dx.doi.org/10.1016/j.jfa.2013.07.001---------- VANCOUVER ----------
Lassalle, S., Turco, P. The Banach ideal of A-compact operators and related approximation properties. J. Funct. Anal. 2013;265(10):2452-2464.
http://dx.doi.org/10.1016/j.jfa.2013.07.001