The Equivalence between Property $(\omega)$ and Weyl's Theorem
Received:December 24, 2009  Revised:May 28, 2010
Key Words: Weyl's theorem   property $(\omega)$   spectrum.  
Fund Project:Supported by Plan of the New Century Talented Person of the Ministry of Education of China (Grant No.NCET-06-0870) and the Fundamental Research Funds for the Central Universities (Grant No.GK200901015).
Author NameAffiliation
Ling Ling ZHAO College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, P. R. China 
Xiao Hong CAO College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, P. R. China 
He Jia ZHANG College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, P. R. China 
Hits: 2660
Download times: 2144
Abstract:
      We call $T\in B(H)$ consistent in Fredholm and index (briefly a CFI operator) if for each $B\in B(H)$, $TB$ and $BT$ are Fredholm together and the same index of $B$, or not Fredholm together. Using a new spectrum defined in view of the CFI operator, we give the equivalence of Weyl's theorem and property $(\omega)$ for $T$ and its conjugate operator $T^*$. In addition, the property $(\omega)$ for operator matrices is considered.
Citation:
DOI:10.3770/j.issn:1000-341X.2011.04.016
View Full Text  View/Add Comment