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arXiv · 2311.14151

Weak Stability and Quasistability

C. S. Kubrusly·P. C. M. Vieira
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Abstract

It is known that weak l-sequential supercyclicity implies weak quasistability, and it is still unknown weather weak l-sequential supercyclicity implies weak stability, much less whether weak supercyclicity implies weak stability (although it is known for a long time that strong supercyclicity implies strong stability). It is shown that weak l-sequential supercyclicity implies weak stability under the assumption of boundedly spaced subsequences. It is given an example of a power bounded quasistable operator which is not weakly stable.

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C. S. Kubrusly, P. C. M. Vieira. 2024-12-17. Weak Stability and Quasistability. https://arxiv.org/abs/2311.14151

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