On p-compact mappings and the p-approximation property
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 a...
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todo:paper_0022247X_v389_n2_p1204_Lassalle2023-10-03T14:29:18Z On p-compact mappings and the p-approximation property Lassalle, S. Turco, P. Approximation properties Holomorphic mappings P-Compact sets 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. Fil:Lassalle, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0022247X_v389_n2_p1204_Lassalle |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Approximation properties Holomorphic mappings P-Compact sets |
| spellingShingle |
Approximation properties Holomorphic mappings P-Compact sets Lassalle, S. Turco, P. On p-compact mappings and the p-approximation property |
| topic_facet |
Approximation properties Holomorphic mappings P-Compact sets |
| description |
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. |
| format |
JOUR |
| author |
Lassalle, S. Turco, P. |
| author_facet |
Lassalle, S. Turco, P. |
| author_sort |
Lassalle, S. |
| title |
On p-compact mappings and the p-approximation property |
| title_short |
On p-compact mappings and the p-approximation property |
| title_full |
On p-compact mappings and the p-approximation property |
| title_fullStr |
On p-compact mappings and the p-approximation property |
| title_full_unstemmed |
On p-compact mappings and the p-approximation property |
| title_sort |
on p-compact mappings and the p-approximation property |
| url |
http://hdl.handle.net/20.500.12110/paper_0022247X_v389_n2_p1204_Lassalle |
| work_keys_str_mv |
AT lassalles onpcompactmappingsandthepapproximationproperty AT turcop onpcompactmappingsandthepapproximationproperty |
| _version_ |
1807316264760115200 |