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- Title
Obstructions for semigroups of partial isometries to be self-adjoint.
- Authors
BERNIK, JANEZ; POPOV, ALEXEY I.
- Abstract
In this paper we study the following question: given a semigroup S of partial isometries acting on a complex separable Hilbert space, when does the selfadjoint semigroup T generated by S again consist of partial isometries? It has been shown by Bernik, Marcoux, Popov and Radjavi that the answer is positive if the von Neumann algebra generated by the initial and final projections corresponding to the members of S is abelian and has finite multiplicity. In this paper we study the remaining case of when this von Neumann algebra has infinite multiplicity and show that, in a sense, the answer in this case is generically negative.
- Subjects
SEMIGROUPS (Algebra); ISOMETRICS (Mathematics); PARTIAL algebras; HILBERT space; VON Neumann algebras; MULTIPLICITY (Mathematics)
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2016, Vol 161, Issue 1, p107
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004116000141