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On compact and bounding holomorphic mappings


Author: Mikael Lindström
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0933517-7
Article copyright: © Copyright 1989 American Mathematical Society

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