Bergman空间上Cowen-Douglas算子的换位

令H~∞(D)表示单位圆盘D上的有界解析函数全体构成的代数,对于■∈H~∞(D),在某种条件下,证明T=M■是一个指标为n的Cowen-Douglaus算子,并且给出了■(T)/rad■(T)可交换的一个充分条件.当n=1时,刻画了T的换位.

The Commutant of Cowen--Douglas Operators on Bergman Space

Let $H^{infty}(D)$denote the algebra of bounded analytic functions on unit disk $D$.For $varphiin H^{infty}(D)$, under some condition, we prove that $T=M^{*}_{varphi}$ is a Cowen--Douglas operator with index $n$, then give a sufficient condition such that $mathscr{ A}'(T)/{rm rad},mathscr{ A}'(T)$ is commutative. For $n=1$, we characterize the commutant of $T$.