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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Invertibility of the commutator of an element in a $C^*$-algebra and its Moore–Penrose inverse

### Tom 200 / 2010

Studia Mathematica 200 (2010), 163-174 MSC: Primary 46L05; Secondary 47B15. DOI: 10.4064/sm200-2-4

#### Streszczenie

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.

#### Autorzy

• Julio BenítezDepartamento de Matemática Aplicada
Instituto de Matemática Multidisciplinar
Camino de Vera s//n
46022, Valencia, Spain
e-mail
Faculty of Science and
Mathematics
University of Niš