Invertibility of the commutator of an element in a C*-algebra and its Moore–Penrose inverse
Julio Benítez, Vladimir Rakočević · Studia Mathematica · 2010
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. Fur