Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Some operator-theoretic calculus for positive definite kernels
HTML articles powered by AMS MathViewer

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 $p$.
References
Similar Articles
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