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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On compact and bounding holomorphic mappings
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by Mikael Lindström
Proc. Amer. Math. Soc. 105 (1989), 356-361
DOI: https://doi.org/10.1090/S0002-9939-1989-0933517-7

Abstract:

Let $E$ and $F$ be complex Banach spaces. We say that a holomorphic mapping $f$ from $E$ into $F$ is compact respectively bounding if $f$ maps some neighbourhood of every point of $E$ into a relatively compact respectively bounding subset of $F$. Recall that a subset of $E$ is bounding if it is mapped onto a bounded set by every complex valued holomorphic mapping on $E$. Compact holomorphic mappings have been studied by R. Aron and M. Schottenloher in [1]. Since every relatively compact subset of a Banach space is trivially bounding it is clear that every compact holomorphic mapping is bounding. We show that the product of three bounding holomorphic mappings is compact.
References
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Bibliographic Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 105 (1989), 356-361
  • MSC: Primary 46G20; Secondary 58C10
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0933517-7
  • MathSciNet review: 933517