Artículo
Polynomials and holomorphic functions on A-compact sets in Banach spaces
Fecha de publicación:
07/2018
Editorial:
Academic Press Inc Elsevier Science
Revista:
Journal of Mathematical Analysis and Applications
ISSN:
0022-247X
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
In this paper we study the behavior of holomorphic mappings on A-compact sets. Motivated by the recent work of Aron, Çalişkan, García 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.
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Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Lassalle, Silvia Beatriz; Turco, Pablo Alejandro; Polynomials and holomorphic functions on A-compact sets in Banach spaces; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 463; 2; 7-2018; 1092-1108
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