Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (5): 1311-1316.

• Articles • Previous Articles     Next Articles

On Operators Satisfying T*|T1+n|2/1+nT&ge|T*|T*|2T

 SHEN Jun-Li1, ZUO Fei2, YANG Chang-Sen2   

  1. 1.Department of Mathematics, Xinxiang University, Henan Xinxiang 453000;
    2.College of Mathematics and Information Science, Henan Normal |University, Henan Xinxiang 453007
  • Received:2009-07-25 Revised:2010-10-22 Online:2011-10-25 Published:2011-10-25
  • Supported by:

    教育部科技司(208081)资助

Abstract:

Let T ∈B(H) be a bounded linear operator on a complex Hilbert space H. In this paper the authors introduce a new class of operator--quasi-*-A(n) and prove some properties of these operators, such as, if T is quasi-*-A(n), then its point spectrum and joint point spectrum are identical. Using these results, the authors also prove that if T or T* is quasi-*-A(n), then the spectral mapping theorem holds for the weyl spectrum and for the essential approximate point spectrum.

Key words: Quasi-*-A(n), Quasisimilarity, Single valued extension property, Weyl spectrum, Essential approximate point spectrum

CLC Number: 

  • 47B20
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