Browsing University of Waterloo by Author "Popov, Alexey I."

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Abelian, amenable operator algebras are similar to C∗ -algebras

Marcoux, Laurent W.; Popov, Alexey I. (Duke University Press, 2016-12)

Suppose that H is a complex Hilbert space and that ℬ(H) denotes the bounded linear operators on H. We show that every abelian, amenable operator algebra is similar to a C∗-algebra. We do this by showing that if 𝒜⊆ℬ(H) is ...
On selfadjoint extensions of semigroups of partial isometries

Bernik, Janez; Marcoux, Laurent W.; Popov, Alexey I.; Radjavi, Heydar (American Mathematical Society, 2016)

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 ...
Ranges of vector states on irreducible operator semigroups

Marcoux, L.W.; Omladič, M.; Popov, A.I.; Radjavi, H.; Yahaghi, B. (Springer, 2016)

Let 𝜑 be a linear functional of rank one acting on an irreducible semigroup S of operators on a finite- or infinite-dimensional Hilbert space. It is a well-known and simple fact that the range of 𝜑 cannot be a singleton. ...