数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1100-1104.doi: 10.1016/S0252-9602(10)60107-5

• 论文 • 上一篇    下一篇

ON REFLEXIVITY OF HYPONORMAL AND WEIGHTED SHIFT OPERATORS

 M. Faghih Ahmadi, K. Hedayatian   

  1. Department of Mathematics, Shiraz University, Shiraz |71454, Iran
  • 收稿日期:2007-09-06 修回日期:2008-08-11 出版日期:2010-07-20 发布日期:2010-07-20
  • 基金资助:

    This research was in part supported by a grant (No. 86-GR-SC-27) from Shiraz University Research Council

ON REFLEXIVITY OF HYPONORMAL AND WEIGHTED SHIFT OPERATORS

 M. Faghih Ahmadi, K. Hedayatian   

  1. Department of Mathematics, Shiraz University, Shiraz |71454, Iran
  • Received:2007-09-06 Revised:2008-08-11 Online:2010-07-20 Published:2010-07-20
  • Supported by:

    This research was in part supported by a grant (No. 86-GR-SC-27) from Shiraz University Research Council

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摘要：

By an elementary proof, we use a result of Conway and Dudziak to show that if A is a hyponormal operator with spectral radius r(A) such that its spectrum is the closed disc {z:|z| ≤ r(A)} then A is reflexive. Using this result,  we give a simple proof of a result of Bercovici, Foias,  and Pearcy on reflexivity of shift operators. Also,  it is shown that every power of an invertible bilateral weighted shift is reflexive.

关键词: Reflexivity of hyponormal operators, bilateral weighted shift, Laurent series

Abstract:

By an elementary proof, we use a result of Conway and Dudziak to show that if A is a hyponormal operator with spectral radius r(A) such that its spectrum is the closed disc {z:|z| ≤ r(A)} then A is reflexive. Using this result,  we give a simple proof of a result of Bercovici, Foias,  and Pearcy on reflexivity of shift operators. Also,  it is shown that every power of an invertible bilateral weighted shift is reflexive.

Key words: Reflexivity of hyponormal operators, bilateral weighted shift, Laurent series

中图分类号: 

  • 47B20
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