An Operator-valued Berezin Transform and the Class of <Emphasis Type="Italic">n</Emphasis>-Hypercontractions |
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Authors: | Anders Olofsson |
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Institution: | (1) Falugatan 22 1tr, SE-113 32 Stockholm, Sweden |
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Abstract: | We study an operator-valued Berezin transform corresponding to certain standard weighted Bergman spaces of square integrable
analytic functions in the unit disc. The study of this operator-valued Berezin transform relates in a natural way to the study
of the class of n-hypercontractions on Hilbert space introduced by Agler. To an n-hypercontraction
we associate a positive
-valued operator measure dω
n, T
supported on the closed unit disc
in a way that generalizes the above notion of operator-valued Berezin transform. This construction of positive operator measures
dω
n, T
gives a natural functional calculus for the class of n-hypercontractions. We revisit also the operator model theory for the class of n-hypercontractions. The new results here concern certain canonical features of the theory. The operator model theory for the
class of n-hypercontractions gives information about the structure of the positive operator measures dω
n, T
. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 47A20 47A25 Secondary 47A45 47B20 |
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