On compact and bounding holomorphic mappings

Mikael LindstrÖm*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)356-361
Number of pages6
JournalProceedings of the American Mathematical Society
Volume105
Issue number2
DOIs
Publication statusPublished - Feb 1989
MoE publication typeA1 Journal article-refereed

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