JIPAM

On Class $wF(p,r,q)$ Operators and Quasisimilarity  
 
  Authors: Changsen Yang, Yuliang Zhao,  
  Keywords: Class $wF(p,r,q)$ operators, Fuglede-Putnam's theorem, Property $(beta)_varepsilon$, Subscalar, Subdecomposable.  
  Date Received: 17/10/06  
  Date Accepted: 15/06/07  
  Subject Codes:

47B20, 47A30.

  
  Editors: Chi-Kwong Li,  
 
  Abstract:

Let $ T$ be a bounded linear operator on a complex Hilbert space $ H$. In this paper, we show that if $ T$ belongs to class $ wF(p,r,q)$ operators, then we have (i) $ T^*X=XN^*$ whenever $ TX=XN$ for some $ Xin B(H)$, where $ N$ is normal and $ X$ is injective with dense range. (ii) $ T$ satisfies the property $ (beta)_varepsilon$, i.e., $ T$ is subscalar, moreover, $ T$ is subdecomposable. (iii) Quasisimilar class $ wF(p,r,q)$ operators have the same spectra and essential spectra. ;


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