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
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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