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Behavior of holomorphic mappings on $ p$-compact sets in a Banach space


Authors: Richard M. Aron, Erhan Çalışkan, Domingo García and Manuel Maestre
Journal: Trans. Amer. Math. Soc. 368 (2016), 4855-4871
MSC (2010): Primary 46G20; Secondary 46B28, 46G25
DOI: https://doi.org/10.1090/tran/6499
Published electronically: October 14, 2015
MathSciNet review: 3456163
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Abstract: We study the behavior of holomorphic mappings on $ p$-compact sets in Banach spaces. We show that the image of a $ p$-compact set by an entire mapping is a $ p$-compact set. Some results related to the localization of $ p$-compact sets in the predual of homogeneous polynomials are also obtained. Finally, the ``size'' of $ p$-compactness of the image of the unit ball by $ p$-compact linear operators is studied.


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Additional Information

Richard M. Aron
Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
Email: aron@math.kent.edu

Erhan Çalışkan
Affiliation: Department of Mathematics, Faculty of Sciences and Arts, Yıldız Technical University, Davutpaşa, 34210 Esenler, İstanbul, Turkey
Email: ercalis@yahoo.com.tr

Domingo García
Affiliation: Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, 46100 Burjasot (Valencia), Spain
Email: domingo.garcia@uv.es

Manuel Maestre
Affiliation: Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, 46100 Burjasot (Valencia), Spain
Email: manuel.maestre@uv.es

DOI: https://doi.org/10.1090/tran/6499
Keywords: Banach spaces, $p$-compact sets, homogeneous polynomials, holomorphic mappings
Received by editor(s): July 24, 2013
Received by editor(s) in revised form: April 15, 2014, and May 26, 2014
Published electronically: October 14, 2015
Additional Notes: The first, third and fourth authors were supported by MICINN Project MTM2011-22417 and by MINECO MTM2014-57838-C2-2-P. The third and fourth authors were also supported by Prometeo II/2013/013. The second author was supported by TÜBİTAK - The Scientific and Technological Research Council of Turkey.
Article copyright: © Copyright 2015 American Mathematical Society

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