Continuity and hypocontinuity for bilinear maps
type: Item
instance of: scholarly article
title: Continuity and hypocontinuity for bilinear maps
zbMATH Open document ID: 0545.46004
DOI: 10.1007/BF01174886
published in: Mathematische Zeitschrift
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173448
review text: Let E, F and G be metric linear spaces and \(b:E\times F\to G\) a separately continuous bilinear map. By employing the notion of K- convergent sequence and K-bounded sets, we give a general hypocontinuity result which holds without completeness assumptions on any of the spaces and which contains the Bourbaki hypocontinuity result for Frechet spaces as a special case. The classical Mazur-Orlicz result on joint continuity is also obtained.
Mathematics Subject Classification ID: 46A20
Mathematics Subject Classification ID: 46M05
zbMATH DE Number: 3867986
zbMATH Keywords: K-convergent sequence
zbMATH Keywords: K-bounded sets
zbMATH Keywords: hypocontinuity
zbMATH Keywords: joint continuity
author: Charles Swartz
MaRDI profile type: Publication
cites work: Q3311107
cites work: The Schur and Phillips lemmas for topological groups
cites work: Über Folgen linearer Operationen
cites work: Q5531981
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description: scientific article; zbMATH DE number 3867986