论文标题
Katznelson-tzafriri定理，用于分析性besov运算符的功能
A Katznelson-Tzafriri theorem for analytic Besov functions of operators
论文作者
论文摘要
让$ t $成为Banach空间上的强力运营商，$ x $，$ \ MATHCAL {a} $是单位光盘$ \ Mathbb {d} $上有界全态函数的Banach代数\ Mathcal {a} $ to有限运算符$ f（t）$上的$ x $。 katznelson-tzafriri类型的定理确定$ \ lim_ {n \ to \ infty} \ | t^n f（t）\ | = 0 $ for functions $ f \ in \ Mathcal {a} $，其边界函数在单一光谱上消失了$σ（t）\ cap \ mathbb {t} $ of $ t $，或者有时满足对光谱合成的更强有力的假设。我们考虑$ \ Mathcal {a} $是Banach代数$ \ Mathcal {B}（\ Mathbb {d}）$的分析性BESOV函数上的$ \ Mathbb {D} $上的情况。我们证明了$ \ Mathcal {b}（\ Mathbb {d}）$的Katznelson-tzafriri定理 - 计算，它扩展了几个先前的结果。
Let $T$ be a power-bounded operator on a Banach space $X$, $\mathcal{A}$ be a Banach algebra of bounded holomorphic functions on the unit disc $\mathbb{D}$, and assume that there is a bounded functional calculus for the operator $T$, so there is a bounded algebra homomorphism mapping functions $f \in \mathcal{A}$ to bounded operators $f(T)$ on $X$. Theorems of Katznelson-Tzafriri type establish that $\lim_{n\to\infty} \|T^n f(T)\| = 0$ for functions $f \in \mathcal{A}$ whose boundary functions vanish on the unitary spectrum $σ(T)\cap \mathbb{T}$ of $T$, or sometimes satisfy a stronger assumption of spectral synthesis. We consider the case when $\mathcal{A}$ is the Banach algebra $\mathcal{B}(\mathbb{D})$ of analytic Besov functions on $\mathbb{D}$. We prove a Katznelson-Tzafriri theorem for the $\mathcal{B}(\mathbb{D})$-calculus which extends several previous results.
