Power-bounded quaternionic operators
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909421563543552 |
|---|---|
| author | Huo, Qinghai Xu, Zhenghua |
| author_facet | Huo, Qinghai Xu, Zhenghua |
| contents | Recently, the conception of slice regular functions was allowed to introduce a new quaternionic functional calculus, among which the theory of semigroups of linear operators was developed into the quaternionic setting, even in a more general case of real alternative $*$-algebras. In this paper, we initiate to study the discrete case and introduce the notion of power-bounded quaternionic operators. In particular, by the spherical Yosida approximation, we establish a discrete Hille-Yosida-Phillips theorem to give an equivalent characterization of quaternionic linear operators being power-bounded. A sufficient condition of the power-boundedness for quaternionic linear operators is also given. In addition, a non-commutative version of the Katznelson-Tzafriri theorem (J. Funct. Anal. 68: 313-328, 1986) for power-bounded quaternionic operators is formulated in terms of the $S$-spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04771 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Power-bounded quaternionic operators Huo, Qinghai Xu, Zhenghua Spectral Theory Recently, the conception of slice regular functions was allowed to introduce a new quaternionic functional calculus, among which the theory of semigroups of linear operators was developed into the quaternionic setting, even in a more general case of real alternative $*$-algebras. In this paper, we initiate to study the discrete case and introduce the notion of power-bounded quaternionic operators. In particular, by the spherical Yosida approximation, we establish a discrete Hille-Yosida-Phillips theorem to give an equivalent characterization of quaternionic linear operators being power-bounded. A sufficient condition of the power-boundedness for quaternionic linear operators is also given. In addition, a non-commutative version of the Katznelson-Tzafriri theorem (J. Funct. Anal. 68: 313-328, 1986) for power-bounded quaternionic operators is formulated in terms of the $S$-spectrum. |
| title | Power-bounded quaternionic operators |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2312.04771 |