Some operatortheoretic calculus for positive definite kernels
Author:
Ameer Athavale
Journal:
Proc. Amer. Math. Soc. 112 (1991), 701708
MSC:
Primary 47B38; Secondary 46E20, 47A57, 47B20, 47B37
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:
http://dx.doi.org/10.1090/S00029939199110681148
PII:
S 00029939(1991)10681148
Keywords:
Positive definite kernel,
hyponormal,
subnormal,
isometry
Article copyright:
© Copyright 1991 American Mathematical Society
