On k-hyperexpansive operators |
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Authors: | George Exner Chunji Li |
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Institution: | a Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA b Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea c Institute of System Science, College of Sciences, Northeastern University, Shenyang, Liaoning 110-004, China |
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Abstract: | This paper considers the k-hyperexpansive Hilbert space operators T (those satisfying , 1?n?k) and the k-expansive operators (those satisfying the above inequality merely for n=k). It is known that if T is k-hyperexpansive then so is any power of T; we prove the analogous result for T assumed merely k-expansive. Turning to weighted shift operators, we give a characterization of k-expansive weighted shifts, and produce examples showing the k-expansive classes are distinct. For a weighted shift W that is k-expansive for all k (that is, completely hyperexpansive) we obtain results for k-hyperexpansivity of back step extensions of W. In addition, we discuss the completely hyperexpansive completion problem which is parallel to Stampfli's subnormal completion problem. |
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Keywords: | Weighted shifts Completely hyperexpansive n-hyperexpansive Subnormal operators |
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