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math.FA2013
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…
math.FA2013
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…
math.FA2013
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…