Year: 2015
Type: preprint
Abstract: An increasing sequence of positive integers $(n_k)_{k\ge 0}$ is said to be a Jamison sequence if the following property holds true: for every separable complex Banach space $X$ and every $T\in \mathcal{B}(X)$ which is partially power-bounded with respect to $(n_k)_{k\ge 0}$, the set $σ_p(T)\cap \T$ is at most countable. We prove that a separable infinite-dimensional complex Banach space $X$ which admits an unconditional Schauder decomposition is such that for any sequence $(n_k)_{k\ge 0}$ which is not a Jamison sequence, there exists $T\in \mathcal{B}(X)$ which is partially power-bounded with respect to this sequence and such that the set $σ_p(T)\cap \T$ is uncountable. We also investigate the notion of Jamison sequences for $C_0$-semigroups and we give an arithmetic characterization of these sequences.
Source: arXiv (Cornell University)
Author: Devinck, Vincent
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2038212403