Moore-Penrose inverse and doubly commuting elements in $C^*$-algebras

Enrico Boasso

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arXiv · 1309.6911

Moore-Penrose inverse and doubly commuting elements in $C^*$-algebras

Enrico Boasso

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Abstract

In this work it is proved that the Moore-Penrose inverse of the product of $n$-doubly commuting regular $C^*$-algebra elements obeys the so-called reverse order law. Conversely, conditions regarding the reverse order law of the Moore-Penrose inverse are given in order to characterize when $n$-regular elements doubly commute. Furthermore, applications of the main results of this article to normal $C^*$-algebra elements, to Hilbert space operators and to Calkin algebras will be considered.

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Enrico Boasso. 2013-09-26. Moore-Penrose inverse and doubly commuting elements in $C^*$-algebras. https://arxiv.org/abs/1309.6911

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