On matrix semigroups bounded above and below
Functional Analysis
2013-06-12 v1 Group Theory
Operator Algebras
Abstract
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 are uniformly bounded above and below, and (b) its idempotents commute. This is a generalization of the well-known result on bounded groups.
Cite
@article{arxiv.1306.1974,
title = {On matrix semigroups bounded above and below},
author = {Alexey I. Popov},
journal= {arXiv preprint arXiv:1306.1974},
year = {2013}
}