Complete hyperexpansivity, subnormality and inverted boundedness conditions |
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Authors: | Zenon J Jaboski |
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Institution: | (1) Instytut Matematyki, Uniwersytet Jagielloski, ul. Reymonta 4, PL-30059 Kraków |
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Abstract: | Athavale introduced in 3] the notion of a completely hyperexpansive operator. In this paper some results concerning powers of completely (alternatingly) hyperexpansive operators (not necessarily bounded) are extended tok-hyperexpansive ones. A semispectral measure is associated with a subnormal contraction as well as with a completely hyperexpansive operator, and an operator version of the Levy-Khinchin representation is obtained. Passing to the Naimark dilation of the semispectral measure, such an operator is related to a positive contraction in a natural way. New characterizations of a completely hyperexpansive operator and a subnormal contraction are given. The power bounded completely hyperexpansive operators are characterized. All these are illustrated using weighted shifts. |
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Keywords: | Primary 47B20 47B37 Secondary 47B40 47B35 |
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