On selfadjoint extensions of semigroups of partial isometries
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Date
2016
Authors
Bernik, Janez
Marcoux, Laurent W.
Popov, Alexey I.
Radjavi, Heydar
Journal Title
Journal ISSN
Volume Title
Publisher
American Mathematical Society
Abstract
Let 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.
Description
First published in Transactions of the American Mathematical Society in volume 368, 2016, published by the American Mathematical Society. https://doi.org/10.1090/tran/6619
Keywords
partial isometry, semigroup, self-adjoint, abelian von Neumann algebra, multiplicity