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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, 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. © 2018 Elsevier Inc.

Registro:

Documento: Artículo
Título:Polynomials and holomorphic functions on A-compact sets in Banach spaces
Autor:Lassalle, S.; Turco, P.
Filiación:Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, Buenos Aires, Victoria B1644BID, Argentina
IMAS – CONICET, Argentina
IMAS – UBA – CONICET – Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Palabras clave:A-compact sets; Banach spaces; Holomorphic functions; Homogeneous polynomials
Año:2018
Volumen:463
Número:2
Página de inicio:1092
Página de fin:1108
DOI: http://dx.doi.org/10.1016/j.jmaa.2018.03.070
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v463_n2_p1092_Lassalle

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Citas:

---------- APA ----------
Lassalle, S. & Turco, P. (2018) . Polynomials and holomorphic functions on A-compact sets in Banach spaces. Journal of Mathematical Analysis and Applications, 463(2), 1092-1108.
http://dx.doi.org/10.1016/j.jmaa.2018.03.070
---------- CHICAGO ----------
Lassalle, S., Turco, P. "Polynomials and holomorphic functions on A-compact sets in Banach spaces" . Journal of Mathematical Analysis and Applications 463, no. 2 (2018) : 1092-1108.
http://dx.doi.org/10.1016/j.jmaa.2018.03.070
---------- MLA ----------
Lassalle, S., Turco, P. "Polynomials and holomorphic functions on A-compact sets in Banach spaces" . Journal of Mathematical Analysis and Applications, vol. 463, no. 2, 2018, pp. 1092-1108.
http://dx.doi.org/10.1016/j.jmaa.2018.03.070
---------- VANCOUVER ----------
Lassalle, S., Turco, P. Polynomials and holomorphic functions on A-compact sets in Banach spaces. J. Math. Anal. Appl. 2018;463(2):1092-1108.
http://dx.doi.org/10.1016/j.jmaa.2018.03.070