Obstructions for semigroups of partial isometries to be self-adjoint
2016 ◽
Vol 161
(1)
◽
pp. 107-116
Keyword(s):
AbstractIn this paper we study the following question: given a semigroup ${\mathcal S}$ of partial isometries acting on a complex separable Hilbert space, when does the selfadjoint semigroup ${\mathcal T}$ generated by ${\mathcal S}$ again consist of partial isometries? It has been shown by Bernik, Marcoux, Popov and Radjavi that the answer is positive if the von Neumann algebra generated by the initial and final projections corresponding to the members of ${\mathcal S}$ is abelian and has finite multiplicity. In this paper we study the remaining case of when this von Neumann algebra has infinite multiplicity and show that, in a sense, the answer in this case is generically negative.
1982 ◽
Vol 34
(6)
◽
pp. 1245-1250
◽
Keyword(s):
2008 ◽
Vol 337
(2)
◽
pp. 1226-1237
◽
Keyword(s):
1979 ◽
Vol 31
(5)
◽
pp. 1012-1016
◽
Keyword(s):
1966 ◽
Vol 18
◽
pp. 897-900
◽
1977 ◽
Vol 81
(2)
◽
pp. 237-243
◽
2007 ◽
Vol 14
(04)
◽
pp. 445-458
◽
Keyword(s):
1975 ◽
Vol 15
(1)
◽
pp. 18-22
◽
1975 ◽
Vol 20
(2)
◽
pp. 159-164