On selfadjoint extensions of semigroups of partial isometries

2014/11/20 by Janez Bernik, Bernik, Janez, Laurent W. Marcoux +5
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Operator Algebras (math.OA) #math.FA #math.GR #math.OA

paper · pdf · doi:10.48550/arxiv.1411.5670

To appear in Transactions of the American Mathematical Society

arxiv created 2014/11/20 · arxiv updated 2014/11/21

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 of final projections of elements of \mathcal S generates an abelian von Neumann algebra of uniform finite multiplicity.

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