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Abstract:

Fixed a Banach operator ideal A, we introduce and investigate two new approximation properties, which are strictly weaker than the bounded approximation property (BAP) for A of Lima et al. (2010). We call them the weak BAP for A and the local BAP for A, showing that the latter is in turn strictly weaker than the former. Under this framework, we address the question of approximation properties passing from dual spaces to underlying spaces. We relate the weak and local BAPs for A with approximation properties given by tensor norms and show that the Saphar BAP of order p is the weak BAP for the ideal of absolutely p*-summing operators, 1≤p≤∞, 1/p+1/p*=1. © 2016 Elsevier Inc.

Registro:

Documento: Artículo
Título:Weaker relatives of the bounded approximation property for a Banach operator ideal
Autor:Lassalle, S.; Oja, E.; Turco, P.
Filiación:Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, Victoria, Buenos Aires, B1644BID, Argentina
IMAS - CONICET, Argentina
Institute of Mathematics and Statistics, University of Tartu, J. Liivi 2, Tartu, 50409, Estonia
Estonian Academy of Sciences, Kohtu 6, Tallinn, 10130, Estonia
IMAS - CONICET, Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Palabras clave:Banach operator ideals; Bounded approximation properties
Año:2016
Volumen:205
Página de inicio:25
Página de fin:42
DOI: http://dx.doi.org/10.1016/j.jat.2016.01.005
Título revista:Journal of Approximation Theory
Título revista abreviado:J. Approx. Theory
ISSN:00219045
CODEN:JAXTA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219045_v205_n_p25_Lassalle

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Citas:

---------- APA ----------
Lassalle, S., Oja, E. & Turco, P. (2016) . Weaker relatives of the bounded approximation property for a Banach operator ideal. Journal of Approximation Theory, 205, 25-42.
http://dx.doi.org/10.1016/j.jat.2016.01.005
---------- CHICAGO ----------
Lassalle, S., Oja, E., Turco, P. "Weaker relatives of the bounded approximation property for a Banach operator ideal" . Journal of Approximation Theory 205 (2016) : 25-42.
http://dx.doi.org/10.1016/j.jat.2016.01.005
---------- MLA ----------
Lassalle, S., Oja, E., Turco, P. "Weaker relatives of the bounded approximation property for a Banach operator ideal" . Journal of Approximation Theory, vol. 205, 2016, pp. 25-42.
http://dx.doi.org/10.1016/j.jat.2016.01.005
---------- VANCOUVER ----------
Lassalle, S., Oja, E., Turco, P. Weaker relatives of the bounded approximation property for a Banach operator ideal. J. Approx. Theory. 2016;205:25-42.
http://dx.doi.org/10.1016/j.jat.2016.01.005