Projective Lie algebra bases of a locally compact group and uniform differentiability
type: Item
instance of: scholarly article
title: Projective Lie algebra bases of a locally compact group and uniform differentiability
zbMATH Open document ID: 0645.22002
DOI: 10.1007/BF01230288
author: Eike Born
published in: Mathematische Zeitschrift
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174008
review text: Let G be a locally compact group and \({\mathcal L}(G)\) its Lie algebra in the sense of R. Lashof. We introduce the notion of a projective basis as a particular vector space basis of \({\mathcal L}(G)\) and prove the existence of such a basis for every locally compact group. From this we obtain results concerning the topological structure of \({\mathcal L}(G)\). Furthermore the existence of a projective basis allows to consider Banach spaces of k- times uniformly differentiable functions on G, containing the space \({\mathcal D}(G)\) of test functions as a dense subspace.
Mathematics Subject Classification ID: 22D05
Mathematics Subject Classification ID: 22D25
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 4051916
zbMATH Keywords: locally compact group
zbMATH Keywords: Lie algebra
zbMATH Keywords: projective basis
zbMATH Keywords: Banach spaces
zbMATH Keywords: uniformly differentiable functions
zbMATH Keywords: testfunctions
Wikidata QID: Q115393821
MaRDI profile type: Publication
cites work: Q3769674
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OpenAlex ID: W2062811545
description: scientific article; zbMATH DE number 4051916