关键词: 强不可约, 双指标Cowen-Douglas 算子, 换位代数, Jacobson 根, K₀群

Abstract:

In the paper,  the authors caculate  the commutant of  Cowen-Douglas operator with two indexes and also the Jacobson radical of the commutant. And it is showed that the commutant of a strongly irreducible Cowen-Douglas operator with two indexes is essentially commutative  by the tools of algebra techniques and spectral theory, and  the K₀ group of the commutant is  isomorphic to the  integer group Z.

Key words: Strongly irreducible,  Cowen-Douglas operator with two indexes,  Commutant algebra, Jacobson radical, K₀ group