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

Aron, Richard; Çalışkan, Erhan; García, Domingo; Maestre, Manuel

doi:10.1090/tran/6499

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.

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