Note on Wermuth's theorem on commuting operator exponentials
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2019
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909570116354048 |
|---|---|
| author | Szczygielski, Krzysztof |
| author_facet | Szczygielski, Krzysztof |
| contents | We apply Wermuth's theorem on commuting operator exponentials to show that if $A, B \in B(X)$, $X$ being Banach space and $A$ of $2πi$-congruence free spectrum, then $e^A B = B e^A$ if and only if $AB=BA$. We employ this observation to provide alternative proof of similar result by Chaban and Mortad, applicable for $X$ being a Hilbert space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_10261 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Note on Wermuth's theorem on commuting operator exponentials Szczygielski, Krzysztof Functional Analysis Operator Algebras Rings and Algebras 47L10, 16S99 We apply Wermuth's theorem on commuting operator exponentials to show that if $A, B \in B(X)$, $X$ being Banach space and $A$ of $2πi$-congruence free spectrum, then $e^A B = B e^A$ if and only if $AB=BA$. We employ this observation to provide alternative proof of similar result by Chaban and Mortad, applicable for $X$ being a Hilbert space. |
| title | Note on Wermuth's theorem on commuting operator exponentials |
| topic | Functional Analysis Operator Algebras Rings and Algebras 47L10, 16S99 |
| url | https://arxiv.org/abs/1901.10261 |