8 citations · 10 across the 6 of their papers we have counts for
13 papers
Isometries of the Toeplitz Matrix Algebra
Douglas Farenick, Mitja Mastnak, Alexey I. Popov
We study the structure of isometries defined on the algebra of upper-triangular Toeplitz matrices. Our first result is that a continuous multiplicative isometry $\mat…
On selfadjoint extensions of semigroups of partial isometries
Janez Bernik, Laurent W. Marcoux, Alexey I. Popov +1
Let 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 t…
Abelian, amenable operator algebras are similar to C*-algebras
Laurent W. Marcoux, Alexey I. Popov
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.…
Semigroups of Partial Isometries
Alexey I. Popov, Heydar Radjavi
We study self-adjoint semigroups of partial isometries on a Hilbert space. These semigroups coincide precisely with faithful representations of abstract inverse semigroups. Groups…
On matrix semigroups bounded above and below
Alexey I. Popov
An irreducible norm closed semigroup of complex matrices is simultaneously similar to a semigroup of partial isometries if and only if (a) the norms of all nonzero members of it ar…
Commutators of small rank and reducibility of operator semigroups
Ali Jafarian, Alexey I. Popov, Mehdi Radjabalipour +1
It is easy to see that if $\cG$ is a non-abelian group of unitary matrices, then for no members and of $\cG$ can the rank of be one. We examine the consequences of…