Some operator-theoretic calculus for positive definite kernels

Author:
Ameer Athavale

Journal:
Proc. Amer. Math. Soc. **112** (1991), 701-708

MSC:
Primary 47B38; Secondary 46E20, 47A57, 47B20, 47B37

DOI:
https://doi.org/10.1090/S0002-9939-1991-1068114-8

MathSciNet review:
1068114

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Abstract: If is a positive definite kernel on the open unit disk in the complex plane, then we associate with it a positive definite kernel on and correlate some operator theoretic properties of and , where denotes the multiplication operator on the functional Hilbert space associated with . The main emphasis of this paper is on the discussion of hyponormality and subnormality properties. We also construct a sequence of positive definite kernels on such that is a -isometry, but not a -isometry for any positive integer less than or equal to .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1068114-8

Keywords:
Positive definite kernel,
hyponormal,
subnormal,
-isometry

Article copyright:
© Copyright 1991
American Mathematical Society