ON REFLEXIVITY OF HYPONORMAL AND WEIGHTED SHIFT OPERATORS |
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Authors: | M. Faghih Ahmadi K. Hedayatian |
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Affiliation: | Department of Mathematics, Shiraz University, Shiraz 71454, Iran |
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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. |
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Keywords: | Reflexivity of hyponormal operators bilateral weighted shift Laurent series |
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