## On selfadjoint extensions of semigroups of partial isometries

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- by Janez Bernik, Laurent W. Marcoux, Alexey I. Popov and Heydar Radjavi PDF
- Trans. Amer. Math. Soc.
**368**(2016), 7681-7702 Request permission

## Abstract:

Let $\mathcal {S}$ be a semigroup of partial isometries acting on a complex, infinite-dimensional, separable Hilbert space. In this paper we seek criteria which will guarantee that the selfadjoint semigroup $\mathcal {T}$ generated by $\mathcal {S}$ consists of partial isometries as well. Amongst other things, we show that this is the case when the set $\mathcal {Q}(\mathcal {S})$ of final projections of elements of $\mathcal {S}$ generates an abelian von Neumann algebra of uniform finite multiplicity.## References

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## Additional Information

**Janez Bernik**- Affiliation: Fakulteta za Matematiko in Fiziko, Univerza v Ljubljani, Jadranska 19, 1000 Ljubljana, Slovenia
- MR Author ID: 713392
- ORCID: 0000-0002-4917-9959
- Email: janez.bernik@fmf.uni-lj.si
**Laurent W. Marcoux**- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- MR Author ID: 288388
- Email: LWMarcoux@uwaterloo.ca
**Alexey I. Popov**- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Address at time of publication: Department of Mathematics & Computer Science, University of Lethbridge, Lethbridge, Alberta T1K 3M4, Canada
- MR Author ID: 775644
- Email: alexey.popov@uleth.ca
**Heydar Radjavi**- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- MR Author ID: 143615
- Email: hradjavi@uwaterloo.ca
- Received by editor(s): September 13, 2013
- Received by editor(s) in revised form: October 19, 2014
- Published electronically: February 25, 2016
- Additional Notes: The research of the first author was supported in part by ARRS (Slovenia)

The research of the second, third, and fourth authors was supported in part by NSERC (Canada) - © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**368**(2016), 7681-7702 - MSC (2010): Primary 47D03; Secondary 47A65, 47B40, 20M20, 46L10
- DOI: https://doi.org/10.1090/tran/6619
- MathSciNet review: 3546779