Invertibility of the commutator of an element in a $C^*$-algebra and its Moore–Penrose inverse
Volume 200 / 2010
Studia Mathematica 200 (2010), 163-174
MSC: Primary 46L05; Secondary 47B15.
DOI: 10.4064/sm200-2-4
Abstract
We study the subset in a unital $C^*$-algebra composed of elements $a$ such that $aa^{\dagger} - a a^{\dagger}$ is invertible, where $a^{\dagger}$ denotes the Moore–Penrose inverse of $a$. A distinguished subset of this set is also investigated. Furthermore we study sequences of elements belonging to the aforementioned subsets.
