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

Volume 200 / 2010

Julio Benítez, Vladimir Rakočević 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.

Authors

  • Julio BenítezDepartamento de Matemática Aplicada
    Instituto de Matemática Multidisciplinar
    Universidad Politécnica de Valencia
    Camino de Vera s//n
    46022, Valencia, Spain
    e-mail
  • Vladimir RakočevićDepartment of Mathematics
    Faculty of Science and
    Mathematics
    University of Niš
    Višegradska, 33
    18000 Niš, Serbia
    e-mail

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