Drazin Invertibility of Operators AB and BA
Received:November 07, 2006  Revised:July 13, 2007
Key Words: Drazin invertibility of operators   Drazin index   Aluthge transforms of operators.  
Fund Project:the National Natural Science Foundation of China (No.10571113).
Author NameAffiliation
LU Jian Ming College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, China 
DU Hong Ke College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, China 
WEI Xiao Mei College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, China 
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Abstract:
      In this note an alternative proof of the equivalence of Drazin invertibility of operators $AB$ and $BA$ is given. As an application, we will prove that $\sigma_D(AB)=\sigma_D(BA)$ and $\sigma_D(A)=\sigma_D(\widetilde{A})$, where $\sigma_D(M)$ and $\widetilde{M}$ denote the Drazin spectrum and the Aluthge transform of an operator $M\in{\cal B}({\cal H})$, respectively.
Citation:
DOI:10.3770/j.issn:1000-341X.2008.04.037
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