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Proceedings of the American Mathematical Society

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



On completely hyperexpansive operators

Author: Ameer Athavale
Journal: Proc. Amer. Math. Soc. 124 (1996), 3745-3752
MSC (1991): Primary 47B20; Secondary 47B39
MathSciNet review: 1353373
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Abstract: We introduce and discuss a class of operators, to be referred to as the class of completely hyperexpansive operators, which is in some sense antithetical to the class of contractive subnormals. The new class is intimately related to the theory of negative definite functions on abelian semigroups. The known interplay between positive and negative definite functions from the theory of harmonic analysis on semigroups can be exploited to reveal some interesting connections between subnormals and completely hyperexpansive operators.

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Ameer Athavale
Affiliation: Department of Mathematics, University of Pune, Pune - 411007, India

Keywords: Positive definite, negative definite, completely monotone, completely alternating, subnormal, completely hyperexpansive
Received by editor(s): May 17, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society