论文标题
Segal-Bargmann空间上的循环构图操作员
Cyclic Composition Operators on Segal-Bargmann space
论文作者
论文摘要
我们研究了segal-bargmann空间上的组合操作员$ c_ϕ $ $ c_ϕ $ $ \ mathscr { \ Mathscr {e} $带有$ \ left \ | a \ right \ | \ leq 1 $和$ a^*b \ in（i-a^*a）^{\ frac {1} {2}}} $。在这方面，我们还给出了符号$ ϕ $的表征，该符号$ ϕ $诱导有限的成分运算符$ c_ϕ $上的$ \ m \ m varyscr {h}（\ mathscr {e}）$，并表明$ ϕ $的属性会影响$ c_ϕ $的环状行为。
We study the hypercyclic, supercyclic and cyclic properties of composition operator $C_ϕ$ on the Segal-Bargmann space $\mathscr{H}(\mathscr{E})$, where $ϕ(z)=Az+b$, $A\in \mathcal{B}(\mathscr{E})$, $b\in \mathscr{E}$ with $\left\|A\right\|\leq 1$ and $A^*b\in (I-A^*A)^{\frac{1}{2}}$. In this connection we also give a characterization of the symbols $ϕ$ which induce the bounded composition operator $C_ϕ$ on $\mathscr{H}(\mathscr{E})$ and show that the properties of $ϕ$ influence the cyclic behaviour of $C_ϕ$.
