算子强不可约的充要条件

The Necessary and Sufficient Condition for Strong Irreducibility of Cowen-Douglas Operators

中文关键词:  强不可约  Cowen-Douglas 算子  换位代数  Jacobson根.

英文关键词:strongly irreducible  Cowen-Douglas operator  commutant algebra  Jacobson radical.

中文摘要:

      本文证明了Cowen-Douglas 算子是强不可约的充要条件,是它的换位代数模去其Jacobson 根同构于$H^{\infty}(D)$中的一个闭子代数,这里$D$表示开单位圆盘, $H^{\infty}(D)$表示$D$上的有界解析函数的全体.

英文摘要:

      In this note, we show that a Cowen-Douglas operator is strongly irreducible if and only if its commutant algebra mod its Jocobson radical is isomorphic to a closed subalgebra of $H^{\infty}(D)$, where $D$ is the open unit disk, and $H^{\infty}(D)$ denotes the collection of bounded holomorphic functions on $D$.