Polynomials and holomorphic functions on A-compact sets in Banach spaces
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...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0022247X_v463_n2_p1092_Lassalle |
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todo:paper_0022247X_v463_n2_p1092_Lassalle2023-10-03T14:29:24Z Polynomials and holomorphic functions on A-compact sets in Banach spaces Lassalle, S. Turco, P. A-compact sets Banach spaces Holomorphic functions Homogeneous polynomials 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0022247X_v463_n2_p1092_Lassalle |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
A-compact sets Banach spaces Holomorphic functions Homogeneous polynomials |
| spellingShingle |
A-compact sets Banach spaces Holomorphic functions Homogeneous polynomials Lassalle, S. Turco, P. Polynomials and holomorphic functions on A-compact sets in Banach spaces |
| topic_facet |
A-compact sets Banach spaces Holomorphic functions Homogeneous polynomials |
| description |
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. |
| format |
JOUR |
| author |
Lassalle, S. Turco, P. |
| author_facet |
Lassalle, S. Turco, P. |
| author_sort |
Lassalle, S. |
| title |
Polynomials and holomorphic functions on A-compact sets in Banach spaces |
| title_short |
Polynomials and holomorphic functions on A-compact sets in Banach spaces |
| title_full |
Polynomials and holomorphic functions on A-compact sets in Banach spaces |
| title_fullStr |
Polynomials and holomorphic functions on A-compact sets in Banach spaces |
| title_full_unstemmed |
Polynomials and holomorphic functions on A-compact sets in Banach spaces |
| title_sort |
polynomials and holomorphic functions on a-compact sets in banach spaces |
| url |
http://hdl.handle.net/20.500.12110/paper_0022247X_v463_n2_p1092_Lassalle |
| work_keys_str_mv |
AT lassalles polynomialsandholomorphicfunctionsonacompactsetsinbanachspaces AT turcop polynomialsandholomorphicfunctionsonacompactsetsinbanachspaces |
| _version_ |
1807315578181910528 |