Geodesic
Invertibility of the commutator of an element in a $C^*$-algebra and its Moore–Penrose inverse
Julio Benítez 1   ; Vladimir Rakočević 2
1 Departamento de Matemática Aplicada Instituto de Matemática Multidisciplinar Universidad Politécnica de Valencia Camino de Vera s//n 46022, Valencia, Spain
2 Department of Mathematics Faculty of Science and Mathematics University of Niš Višegradska, 33 18000 Niš, Serbia
Studia Mathematica, Tome 200 (2010) no. 2, pp. 163-174 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm200-2-4
Keywords: study subset unital * algebra composed elements dagger dagger invertible where dagger denotes moore penrose inverse distinguished subset set investigated furthermore study sequences elements belonging aforementioned subsets

Julio Benítez  1   ; Vladimir Rakočević  2

1 Departamento de Matemática Aplicada Instituto de Matemática Multidisciplinar Universidad Politécnica de Valencia Camino de Vera s//n 46022, Valencia, Spain
2 Department of Mathematics Faculty of Science and Mathematics University of Niš Višegradska, 33 18000 Niš, Serbia 
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Julio Benítez; Vladimir Rakočević. Invertibility of the commutator of an element
 in a $C^*$-algebra and its Moore–Penrose inverse. Studia Mathematica, Tome 200 (2010) no. 2, pp. 163-174. doi: 10.4064/sm200-2-4

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