A -compact mappings
For a fixed Banach operator ideal A, we use the notion of A-compact sets of Carl and Stephani to study A-compact polynomials and A-compact holomorphic mappings. Namely, those mappings g: X→ Y such that every x∈ X has a neighborhood V x such that g(V x ) is relatively A-compact. We show that the beha...
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_15787303_v110_n2_p863_Turco |
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| Sumario: | For a fixed Banach operator ideal A, we use the notion of A-compact sets of Carl and Stephani to study A-compact polynomials and A-compact holomorphic mappings. Namely, those mappings g: X→ Y such that every x∈ X has a neighborhood V x such that g(V x ) is relatively A-compact. We show that the behavior of A-compact polynomials is determined by its behavior in any neighborhood of any point. We transfer some known properties of A-compact operators to A-compact polynomials. In order to study A-compact holomorphic functions, we appeal to the A-compact radius of convergence which allows us to characterize the functions in this class. Under certain hypothesis on the ideal A, we give examples showing that our characterization is sharp. © 2015, Springer-Verlag Italia. |
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