【摘要】 设H是一个可分的Hilbert空间,(?)(H)是H上的有界线性算子全体．对 A∈(?)(H),(?)’(A)={B∈(?)(H):AB=BA},rad(?)’(A)表示(?)’(A)的Jacob son根．本文首先举例说明了存在Cowen-Douglas算子T,商代数(?)’(T)／rad(?)’(T) 可以是不交换的．在给出了使得(?)’(T)／rad(?)’(T)交换的充分条件之后,证明了使得 (?)’(T)／rad(?)’(T)交换的Cowen-Douglas算子在Bn(Ω)中是稠密的．对Bmn(Ω),得到了类似的结果。更多还原

【Abstract】 Let H be a complex seperable Hilbert space and L(H) denote the collection of bounded linear operators on H. In this paper, we first show that the quotient algebra (?)’(T)/rad(?)’(T) is not always commutative for each T ∈ Bn(Ω). Then after giving a sufficient condition for (?)’(T)/rad.(?)’(T) to be commutative, we show that the set of ,Bbn(Ω) operators A, with (?)’(A)/rad(?)’(A) commutative, is dense in Bn(Ω). Similar results are also established for Bmn(Ω) operators.更多还原