Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (2): 272-282.

• Articles • Previous Articles     Next Articles

Drazin Spectra of 2×2 Upper-triangular |Operator Matrices

 ZHANG Hai-Yan, ZHANG Xi-Hua, DU Hong-Ke   

  1. (1. Department |of |Mathematics, Shangqiu Normal College, Henan Shangqiu 476000|2. College of Mathematics and Information Science, |Shaanxi Normal University, Xi'an 710062)
  • Received:2007-11-30 Revised:2008-11-08 Online:2009-04-25 Published:2009-04-25
  • Supported by:

    国家自然科学基金(10871224)和河南省教育厅自然科学研究计划(2008B110014)资助

Abstract:

Let MC=[A   C ;  0   B] be a 2×2 upper-triangular  operator matrix acting on the  Hilbert space H  K .  In this paper, the authors investigate the Drazin invertibility of MC and the Drazin spectrum of MC. Moreover,  for given operaters B}(H) and  B ∈B}(K), they shall give a  representation of ∩ σD (MC) under  certain condition.

Key words: Drazin spectrum, Upper-triangular , operator matrix, Ascent, Descent

CLC Number: 

  • 47A05
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