Moore-Penrose inversion in complex contracted inverse semigroup algebras
Walter Douglas Munn · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1999
Abstract It is shown that every element of the complex contracted semigroup algebra of an inverse semigroup S = S0 has a Moore-Penrose inverse, with respect to the natural involution, if and only if S is locally finite. In particular, every element of a complex group algebra has such an inverse if and only if the group is locally finite.