When locally contractive representations are completely contractive
type: Item
instance of: scholarly article
title: When locally contractive representations are completely contractive
zbMATH Open document ID: 0871.47009
author: Kenneth R. Davidson
published in: Journal of Functional Analysis
publication date: 1997-10-06T00:00:00Z
review text: The representation theory of non-self-adjoint matrix algebras is explored. A representation is called locally contractive if each matrix unit is sent to a contraction. The class of finite dimensional algebras for which every locally contractive representation of the enveloping \(C^*\)-algebra coincides with the class of finite dimensional algebras for which locally contractive representations are contractive. A lattice theoretic characterization of this class is obtained. A matrix algebra containing the diagonal algebra is classified by a directed graph depending on the matrix units in the algebra. There is given also a lattice theoretic characterization of algebras for which the commutant lifting theorem is valid. The results are generalized to infinite dimensional commutative subspace lattice algebras.
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 46K10
Mathematics Subject Classification ID: 46K50
zbMATH DE Number: 764005
zbMATH Keywords: unitary \(*\)-dilation
zbMATH Keywords: non-self-adjoint matrix algebras
zbMATH Keywords: finite dimensional algebras
zbMATH Keywords: locally contractive representation
zbMATH Keywords: enveloping \(C^*\)-algebra
zbMATH Keywords: lattice theoretic characterization
zbMATH Keywords: diagonal algebra
zbMATH Keywords: directed graph
zbMATH Keywords: commutant lifting theorem
zbMATH Keywords: infinite dimensional commutative subspace lattice algebras
MaRDI profile type: Publication
full work available at URL: jfan.1995.1028
OpenAlex ID: W2037815131
DOI: 10.1006/JFAN.1995.1028
description: scientific article; zbMATH DE number 764005