Pure Semigroups of Isometries on Hilbert C*-Modules
Operator Algebras
2016-07-29 v2 Functional Analysis
Abstract
We show that pure strongly continuous semigroups of adjointable isometries on a Hilbert C*-module are standard right shifts. By counter examples, we illustrate that the analogy of this result with the classical result on Hilbert spaces by Sz.-Nagy, cannot be improved further to understand arbitrary isometry semigroups of isometries in the classical way.
Cite
@article{arxiv.1408.2631,
title = {Pure Semigroups of Isometries on Hilbert C*-Modules},
author = {B. V. Rajarama Bhat and Michael Skeide},
journal= {arXiv preprint arXiv:1408.2631},
year = {2016}
}
Comments
18 pages; correction of an awful lot of typos; avoiding in some places a conflict with the known terminology 'reducing subspace'