On selfadjoint extensions of semigroups of partial isometries

Bernik, Janez; Marcoux, Laurent; Popov, Alexey; Radjavi, Heydar

doi:10.1090/tran/6619

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.

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