में बचाया:
| मुख्य लेखक: | |
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| स्वरूप: | Preprint |
| प्रकाशित: |
2018
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| विषय: | |
| ऑनलाइन पहुंच: | https://arxiv.org/abs/1802.01007 |
| टैग: |
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| _version_ | 1866912347331756032 |
|---|---|
| author | Pietrzycki, Paweł |
| author_facet | Pietrzycki, Paweł |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1802_01007 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Reduced commutativity of moduli of operators Pietrzycki, Paweł Functional Analysis 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. |
| title | Reduced commutativity of moduli of operators |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/1802.01007 |