Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (6): 1435-1443.

• Articles • Previous Articles     Next Articles

The Commutant of Bm, n(Ω) and Its K0 Group

 HE Hua, HAN Bing, DONG Yun-Bai   

  1. Department of Mathematics, Hebei University of Technology, Tianjin 300130|Department of Mathematical Sciences, Xiamen University, Fujian Xiamen 361005
  • Received:2007-11-12 Revised:2009-09-16 Online:2010-12-25 Published:2010-12-25
  • Supported by:

    国家自然科学基金(10571041)和河北省自然科学基金(A2005000006)资助

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

CLC Number: 

  • 47A15
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