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Abstract:

The notion of p-compact sets arises naturally from Grothendieck's characterization of compact sets as those contained in the convex hull of a norm null sequence. The definition, due to Sinha and Karn (2002), leads to the concepts of p-approximation property and p-compact operators (which form an ideal with its ideal norm κ p). This paper examines the interaction between the p-approximation property and certain space of holomorphic functions, the p-compact analytic functions. In order to understand these functions we define a p-compact radius of convergence which allows us to give a characterization of the functions in the class. We show that p-compact holomorphic functions behave more like nuclear than compact maps. We use the ε-product of Schwartz, to characterize the p-approximation property of a Banach space in terms of p-compact homogeneous polynomials and in terms of p-compact holomorphic functions with range on the space. Finally, we show that p-compact holomorphic functions fit into the framework of holomorphy types which allows us to inspect the κ p-approximation property. Our approach also allows us to solve several questions posed by Aron, Maestre and Rueda (2010). © 2012 Elsevier Inc.

Registro:

Documento: Artículo
Título:On p-compact mappings and the p-approximation property
Autor:Lassalle, S.; Turco, P.
Filiación:Departamento de Matemática, Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
IMAS, CONICET, Argentina
Palabras clave:Approximation properties; Holomorphic mappings; P-Compact sets
Año:2012
Volumen:389
Número:2
Página de inicio:1204
Página de fin:1221
DOI: http://dx.doi.org/10.1016/j.jmaa.2011.12.058
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0022247X_v389_n2_p1204_Lassalle.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v389_n2_p1204_Lassalle

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Citas:

---------- APA ----------
Lassalle, S. & Turco, P. (2012) . On p-compact mappings and the p-approximation property. Journal of Mathematical Analysis and Applications, 389(2), 1204-1221.
http://dx.doi.org/10.1016/j.jmaa.2011.12.058
---------- CHICAGO ----------
Lassalle, S., Turco, P. "On p-compact mappings and the p-approximation property" . Journal of Mathematical Analysis and Applications 389, no. 2 (2012) : 1204-1221.
http://dx.doi.org/10.1016/j.jmaa.2011.12.058
---------- MLA ----------
Lassalle, S., Turco, P. "On p-compact mappings and the p-approximation property" . Journal of Mathematical Analysis and Applications, vol. 389, no. 2, 2012, pp. 1204-1221.
http://dx.doi.org/10.1016/j.jmaa.2011.12.058
---------- VANCOUVER ----------
Lassalle, S., Turco, P. On p-compact mappings and the p-approximation property. J. Math. Anal. Appl. 2012;389(2):1204-1221.
http://dx.doi.org/10.1016/j.jmaa.2011.12.058