Unitary dilations and the \(C^ *\)-algebra \({\mathcal O}_ 2\)
type: Item
instance of: scholarly article
title: Unitary dilations and the \(C^ *\)-algebra \({\mathcal O}_ 2\)
zbMATH Open document ID: 0636.46052
DOI: 10.1007/BF02766120
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Unitary \(2\times 2\) matrices of operators are studied. Unitary dilations of isometries T reduce to the case where the upper left corner is T and the lower left corner is 0. A unitary dilation is the minimal unitary power dilation of the given isometry if and only if the lower right corner is the adjoint of a unilateral shift. Also the order properties of the set of all unitary dilations of a given nonunitary isometry are considered. Let \({\mathcal A}\) be the \(C^*\)- algebra generated by the upper right and lower right corners in a \(2\times 2\) matrix which is a unitary dilation of a given isometry T. Let I be the ideal generated by the complementary projection to the defect projection of T. Then either \(I=A\) or the quotient A/I is isomorphic to the Cuntz algebra \({\mathcal O}_ 2\).
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 47A20
zbMATH DE Number: 4036496
zbMATH Keywords: Unitary dilations of isometries
zbMATH Keywords: minimal unitary power dilation
zbMATH Keywords: lower right corner
zbMATH Keywords: unilateral shift
zbMATH Keywords: Cuntz algebra
author: Palle Jorgensen
reviewed by: Tage Bai Andersen
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02766120
OpenAlex ID: W2004905586
description: scientific article; zbMATH DE number 4036496