Pure Semigroups of Isometries on Hilbert C*-Modules

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.

18 pages; correction of an awful lot of typos; avoiding in some places a conflict with the known terminology 'reducing subspace'

References in corpus (1)

• Von Neumann Modules, Intertwiners and Self-Duality

Cited by in corpus (2)

• CP-Semigroups and Dilations, Subproduct Systems and Superproduct Systems: The Multi-Parameter Case and Beyond
• Kernels of Hilbert Module Maps: A Counterexample