A non spatial continuous semigroup of *-endomorphisms of \({\mathcal B}({\mathcal H})\)
type: Item
instance of: scholarly article
title: A non spatial continuous semigroup of *-endomorphisms of \({\mathcal B}({\mathcal H})\)
zbMATH Open document ID: 0651.47025
author: Robert T. Powers
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1987-01-01T00:00:00Z
review text: In his paper ``An index theory fo semigroups of *-endomorphisms of B(\({\mathcal B})\) and type II, factors'' [Can. J. Math. 40, No.1, 86-114 (1988; Zbl 0632.46048)], \textit{R. Powers} associated an index with continuous one parameter semigroups \(\alpha_ t\) of *-endomorphisms of B(\({\mathcal B})\) having an interwining semigroup of isometrics, that is, there is strongly continuous semigroup of isometrics U(t)\(\in B({\mathcal B})\) so that \(U(t)A=\alpha_ t(A)U(t)\) for all \(A\in B({\mathcal B})\). He raised the question of whether such an intertwining semigroup of isometrics always exists. In this paper he constructs a continuous one parameter semigroup \(\alpha_ t\) of *-endomorphisms of B(\({\mathcal B})\) having the property that there does not exist a strongly continuous one parameter semigroup of intertwining isometrics. The construction is technical and uses quasi-free states of CAR algebras and almost multiplication operators.
reviewed by: Wu Liangsen
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 4061983
zbMATH Keywords: *-endomorphisms
zbMATH Keywords: continuous one parameter semigroup of intertwining isometrics
zbMATH Keywords: quasi-free states of CAR algebras
zbMATH Keywords: almost multiplication operators
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195175872
OpenAlex ID: W1882874209
cites work: REPRESENTATIONS OF THE ANTICOMMUTATION RELATIONS
cites work: Free states of the canonical anticommutation relations
DOI: 10.2977/PRIMS/1195175872
description: scientific article; zbMATH DE number 4061983