info:eu-repo/semantics/article
On p-compact mappings and the p-approximation property
Fecha
2012-05Registro en:
Lassalle, Silvia Beatriz; Turco, Pablo Alejandro; On p-compact mappings and the p-approximation property; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 389; 2; 5-2012; 1204-1221
0022-247X
CONICET Digital
CONICET
Autor
Lassalle, Silvia Beatriz
Turco, Pablo Alejandro
Resumen
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 κp). 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 κp-approximation property. Our approach also allows us to solve several questions posed by Aron, Maestre and Rueda (2010).