Behavior of holomorphic mappings on $p$-compact sets in a Banach space
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- by Richard M. Aron, Erhan Çalışkan, Domingo García and Manuel Maestre PDF
- Trans. Amer. Math. Soc. 368 (2016), 4855-4871 Request permission
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.References
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Additional Information
- Richard M. Aron
- Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
- MR Author ID: 27325
- 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
- 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.
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 4855-4871
- MSC (2010): Primary 46G20; Secondary 46B28, 46G25
- DOI: https://doi.org/10.1090/tran/6499
- MathSciNet review: 3456163