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 conditi...

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Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis Vol. 3; no. 3; pp. 245 - 257
Main Authors: Athavale, Ameer, Sholapurkar, V.M.
Format: Journal Article
Language:English
Published: Dordrecht Springer Nature B.V 01.09.1999
Subjects:
Commuting
Geometry
Hilbert space
Mathematical functions
Mathematical models
Studies
Theory
Asia
ISSN:1385-1292, 1572-9281
Online Access:Get full text
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Summary: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. [PUBLICATION ABSTRACT]
Bibliography:SourceType-Scholarly Journals-1
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ISSN:1385-1292
1572-9281
DOI:10.1023/A:1009719803199