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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some operator-theoretic calculus for positive definite kernels
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by Ameer Athavale PDF
Proc. Amer. Math. Soc. 112 (1991), 701-708 Request permission

Abstract:

If $\kappa$ is a positive definite kernel on the open unit disk $D$ in the complex plane, then we associate with it a positive definite kernel $\kappa ’$ on $D$ and correlate some operator theoretic properties of $M\left ( \kappa \right )$ and $M\left ( {\kappa ’} \right )$, where $M\left ( \kappa \right )$ denotes the multiplication operator on the functional Hilbert space $\mathcal {H}\left ( \kappa \right )$ associated with $\kappa$. The main emphasis of this paper is on the discussion of hyponormality and subnormality properties. We also construct a sequence of positive definite kernels ${\kappa _{ - p}}\left ( {p = 1,2, \ldots } \right )$ on $D$ such that $M\left ( {{\kappa _{ - p}}} \right )$ is a $\left ( {p + 1} \right )$-isometry, but not a $q$-isometry for any positive integer $q$ less than or equal to $p$.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • 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