Completely Hyperexpansive Operator Tuples

Completely Hyperexpansive Operator Tuples The notion of a completely hyperexpansive operator on a Hilbert space is generalized to that of a completely hyperexpansive operator tuple, which in some sense turns out to be antithetical to the notion of a subnormal operator tuple with contractive coordinates. The countably many negativity conditions characterizing a completely hyperexpansive operator tuple are closely related to the Levy–Khinchin representation in the theory of harmonic analysis on semigroups. The interplay between the theories of positive and negative definite functions on semigroups forces interesting connections between the classes of subnormal and completely hyperexpansive operator tuples. Further, the several–variable generalization allows for a stimulating interaction with the multiparameter spectral theory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Completely Hyperexpansive Operator Tuples

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 1999 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1009719803199
Publisher site
See Article on Publisher Site

Abstract

The notion of a completely hyperexpansive operator on a Hilbert space is generalized to that of a completely hyperexpansive operator tuple, which in some sense turns out to be antithetical to the notion of a subnormal operator tuple with contractive coordinates. The countably many negativity conditions characterizing a completely hyperexpansive operator tuple are closely related to the Levy–Khinchin representation in the theory of harmonic analysis on semigroups. The interplay between the theories of positive and negative definite functions on semigroups forces interesting connections between the classes of subnormal and completely hyperexpansive operator tuples. Further, the several–variable generalization allows for a stimulating interaction with the multiparameter spectral theory.

Journal

PositivitySpringer Journals

Published: Oct 16, 2004

References

  • On completely hyperexpansive operators
    Athavale, A.

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