Bernik, JanezMarcoux, Laurent W.Popov, Alexey I.Radjavi, Heydar2020-04-012020-04-012016https://doi.org/10.1090/tran/6619http://hdl.handle.net/10012/15729First published in Transactions of the American Mathematical Society in volume 368, 2016, published by the American Mathematical Society. https://doi.org/10.1090/tran/6619Let 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 T generated by S consists of partial isometries as well. Amongst other things, we show that this is the case when the set Q(S) of final projections of elements of S generates an abelian von Neumann algebra of uniform finite multiplicity.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/partial isometrysemigroupself-adjointabelian von Neumann algebramultiplicityArticle