Schwartz spaces and compact holomorphic mappings
type: Item
instance of: scholarly article
title: Schwartz spaces and compact holomorphic mappings
zbMATH Open document ID: 0653.46008
DOI: 10.1007/BF01161925
author: Mikael Lindström
published in: Manuscripta Mathematica
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155272
review text: Let E be a quasi-normable locally convex space. The following statements are proved equivalent: (a) E is a Schwartz space; (b) Every equicontinuous weak*-null sequence in the dual of E is strongly null; (c) Every continuous linear mapping of E into \(c_ 0\) is compact; (d) Every holomorphic mapping of E into \(c_ 0\) is compact.
Mathematics Subject Classification ID: 46A13
Mathematics Subject Classification ID: 46A11
Mathematics Subject Classification ID: 47B06
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 4065657
zbMATH Keywords: compact holomorphic mappings
zbMATH Keywords: quasi-normable locally convex space
zbMATH Keywords: Schwartz space
zbMATH Keywords: equicontinuous weak*-null sequence in the dual
MaRDI profile type: Publication
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OpenAlex ID: W181067469
description: scientific article; zbMATH DE number 4065657