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arXiv · 1802.01007

Reduced commutativity of moduli of operators

Paweł Pietrzycki
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Abstract

In this paper, we investigate the question of when the equations $A^{*s}A^{s}=(A^{*}A)^{s}$ for all $s \in S$, where $S$ is a finite set of positive integers, imply the quasinormality or normality of $A$. In particular, it is proved that if $S=\{p,m,m+p,n,n+p\}$, where $2\leq m < n$, then $A$ is quasinormal. Moreover, if $A$ is invertible and $S=\{m,n,n+m\}$, where $m \leq n$, then $A$ is normal. Furthermore, the case when $S=\{m,m+n\}$ and $A^{*n}A^n \leq (A^*A)^n$ is discussed.

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Paweł Pietrzycki. 2018-02-03. Reduced commutativity of moduli of operators. https://doi.org/10.1016/j.laa.2018.08.007

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