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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Vydáno v:Positivity : an international journal devoted to the theory and applications of positivity in analysis Ročník 3; číslo 3; s. 245 - 257
Hlavní autoři: Athavale, Ameer, Sholapurkar, V.M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Nature B.V 01.09.1999
Témata:
Commuting
Geometry
Hilbert space
Mathematical functions
Mathematical models
Studies
Theory
Asia
ISSN:1385-1292, 1572-9281
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Popis
Shrnutí: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]
Bibliografie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1385-1292
1572-9281
DOI:10.1023/A:1009719803199