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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.04771 |
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Table of 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.