Elements of C*-algebras commuting with their Moore-Penrose inverse

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Factorizations of EP operators (2008, methodology): “This result was extended to operators on a Hilbert space by Fildan in [9] (see also [3]), to elements of C∗algebras by Harte and Mbekhta in [11] and by Koliha in [17] and to elements of rings by Hartwig in [13,14].”
T-Jordan Canonical Form and T-Drazin Inverse Based on the T-Product (2019, background): “e the two typical kinds of generalized inverses people usually use and research in matrix theories and associative ring theories. In 1999, the Drazin inverse was even extended to C-algebras by Koliha [36, 37]. The Drazin inverse is proved to be useful in Markov chain, matrix dierential equations and”
EP elements in rings (2009, unknown): “The EP matrices and EP linear operators on Banach or Hilbert spaces have been investigated by many authors (see, for example, [1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 17, 18, 21]).”
Elements of rings with equal spectral idempotents (2002, methodology): “The concept has been studied recently in the setting of C∗-algebras [ 10 ].”
Characterizations of normal, hyponormal and EP operators (2007, background): “The notion of EP operators in well-known (see [2, 3, 6, 7, 8, 9, 16, 17, 18, 19, 20]).”