کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6419289 | 1339390 | 2012 | 18 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: On p-compact mappings and the p-approximation property On p-compact mappings and the p-approximation property](/preview/png/6419289.png)
The notion of p-compact sets arises naturally from Grothendieckʼs 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).
Journal: Journal of Mathematical Analysis and Applications - Volume 389, Issue 2, 15 May 2012, Pages 1204-1221