A note on the positivity of inverse operators acting on $C^*$-algebras
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913420600672256 |
|---|---|
| author | Glück, Jochen Groh, Ulrich |
| author_facet | Glück, Jochen Groh, Ulrich |
| contents | For a positive and invertible linear operator $T$ acting on a $C^*$-algebra, we give necessary and sufficient criteria for the inverse operator $T^{-1}$ to be positive, too. Moreover, a simple counterexample shows that $T^{-1}$ need not be positive even if $T$ is unital and its spectrum is contained in the unit circle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05403 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the positivity of inverse operators acting on $C^*$-algebras Glück, Jochen Groh, Ulrich Operator Algebras Functional Analysis Spectral Theory 37A55, 46L40, 46L55, 47B65 For a positive and invertible linear operator $T$ acting on a $C^*$-algebra, we give necessary and sufficient criteria for the inverse operator $T^{-1}$ to be positive, too. Moreover, a simple counterexample shows that $T^{-1}$ need not be positive even if $T$ is unital and its spectrum is contained in the unit circle. |
| title | A note on the positivity of inverse operators acting on $C^*$-algebras |
| topic | Operator Algebras Functional Analysis Spectral Theory 37A55, 46L40, 46L55, 47B65 |
| url | https://arxiv.org/abs/2407.05403 |