$C_0$ -半群的泛Jamison空间和Jamison序列
Universal Jamison spaces and Jamison sequences for $C_0$-semigroups
摘要：
正整数递增序列$(n_k)_{k\ge 0}$称为Jamison序列，如果以下性质成立：对于每个可分复巴拿赫空间$X$和每个关于$(n_k)_{k\ge 0}$部分幂有界的$T\in \mathcal{B}(X)$，集合$σ_p(T)\cap \T$至多可数。证明了可分无限维复巴拿赫空间$X$允许无条件Schauder分解，使得对于任何非Jamison序列的序列$(n_k)_{k\ge 0}$，存在关于该序列部分幂有界的$T\in \mathcal{B}(X)$，且集合$σ_p(T)\cap \T$是不可数的.我们还研究了$C_0$ -半群的Jamison序列的概念，并给出了这些序列的算术刻画。
英文摘要：
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.
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