Invariant dissipative operators on locally compact groups
type: Item
instance of: scholarly article
title: Invariant dissipative operators on locally compact groups
zbMATH Open document ID: 0608.47037
DOI: 10.1007/BF01163652
author: Hiroshi Nakazato
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173872
review text: Let G be a Lie group and \(C_ 0(G)\) the Banach space of all continuous functions on G vanishing at infinity. In this note we show that if the Lie algebra of G is not compact, then the closure \=D of a left invariant elliptic differential operator D on G has a restriction T such that T is also a left invariant closed dissipative linear operator in \(C_ 0(G)\) satisfying the inequality \(Range(I-T)\subsetneqq c_ 0(G)\).
Mathematics Subject Classification ID: 47B44
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 3983935
zbMATH Keywords: Lie group
zbMATH Keywords: Lie algebra
zbMATH Keywords: left invariant elliptic differential operator
zbMATH Keywords: closed dissipative linear operator
MaRDI profile type: Publication
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OpenAlex ID: W1976927508
description: scientific article; zbMATH DE number 3983935