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Abstract In this paper we study the behavior of holomorphic mappings on A -compact sets. Motivated by the recent work of Aron, Caliskan, Garcia and Maestre (2016), we give several… Click to show full abstract
Abstract In this paper we study the behavior of holomorphic mappings on A -compact sets. Motivated by the recent work of Aron, Caliskan, Garcia and Maestre (2016), we give several conditions (on the holomorphic mappings and on the λ-Banach operator ideal A ) under which A -compact sets are preserved. Appealing to the notion of tensor stability for operator ideals, we first address the question in the polynomial setting. Then, we define a radius of ( A ; B ) -compactification that permits us to tackle the analytic case. Our approach, for instance, allows us to show that the image of any ( p , r ) -compact set under any holomorphic function (defined on any open set of a Banach space) is again ( p , r ) -compact.
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2018
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