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Carando, D.; Mazzitelli, M. "Bounded holomorphic functions attaining their norms in the bidual" (2015) Publications of the Research Institute for Mathematical Sciences. 51(3):489-512
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Abstract:

Under certain hypotheses on the Banach space X, we prove that the set of analytic functions in Au(X) (the algebra of all holomorphic and uniformly continuous functions in the ball of X) whose Aron-Berner extensions attain their norms is dense in Au (X). This Lindenstrauss type result also holds for functions with values in a dual space or in a Banach space with the so-called property (β). We show that the Bishop-Phelps theorem does not hold for Au(co, Z") for a certain Banach space Z, while our Lindenstrauss theorem does. In order to obtain our results, we first handle their polynomial cases. © 2015 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.

Registro:

Documento: Artículo
Título:Bounded holomorphic functions attaining their norms in the bidual
Autor:Carando, D.; Mazzitelli, M.
Filiación:Departamento de Matemática - Pab I, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Palabras clave:Integral formula; Lindenstrauss type theorems; Norm attaining holomorphic mappings
Año:2015
Volumen:51
Número:3
Página de inicio:489
Página de fin:512
DOI: http://dx.doi.org/10.4171/PRIMS/162
Título revista:Publications of the Research Institute for Mathematical Sciences
Título revista abreviado:Publ. Res. Inst. Math. Sci.
ISSN:00345318
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00345318_v51_n3_p489_Carando

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Citas:

---------- APA ----------
Carando, D. & Mazzitelli, M. (2015) . Bounded holomorphic functions attaining their norms in the bidual. Publications of the Research Institute for Mathematical Sciences, 51(3), 489-512.
http://dx.doi.org/10.4171/PRIMS/162
---------- CHICAGO ----------
Carando, D., Mazzitelli, M. "Bounded holomorphic functions attaining their norms in the bidual" . Publications of the Research Institute for Mathematical Sciences 51, no. 3 (2015) : 489-512.
http://dx.doi.org/10.4171/PRIMS/162
---------- MLA ----------
Carando, D., Mazzitelli, M. "Bounded holomorphic functions attaining their norms in the bidual" . Publications of the Research Institute for Mathematical Sciences, vol. 51, no. 3, 2015, pp. 489-512.
http://dx.doi.org/10.4171/PRIMS/162
---------- VANCOUVER ----------
Carando, D., Mazzitelli, M. Bounded holomorphic functions attaining their norms in the bidual. Publ. Res. Inst. Math. Sci. 2015;51(3):489-512.
http://dx.doi.org/10.4171/PRIMS/162