Generalized multipliers for left-invertible analytic operators and their applications to commutant and reflexivity |
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Authors: | P. Dymek A. Płaneta M. Ptak |
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Affiliation: | Katedra Zastosowań Matematyki, Uniwersytet Rolniczy w Krakowie, ul. Balicka 253c, 30-198 Kraków, Poland |
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Abstract: | We introduce generalized?multipliers for?left-invertible analytic operators. We show that they form a Banach algebra and characterize the commutant of such operators in its terms. In the special case, we describe the commutant of balanced weighted shift only in terms of its weights. In addition, we prove two independent criteria for reflexivity of weighted shifts on directed trees. |
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Keywords: | 47A45 47B37 Weighted shift on directed tree Generalized multiplier Commutant Reflexivity |
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