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. ...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.展开更多
基金supported by a grant (No.86-GR-SC-27) from Shiraz University Research Council
文摘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.
