Stability of Jamison sequences under certain perturbations

Abstract

An increasing sequence of positive integers \((n_k)\) is said to be Jamison if whenever \(T\) is a linear bounded operator on a complex separable Banach space, the following holds : \[\sup_{k}||T^{n_k}||<\infty \Rightarrow \sigma_{p}(T)\cap S^1 \text{ is countable}\] In this paper, we study certain perturbations on the set of Jamison sequences and prove a stability result.