A note on joint hyponormality

McCullough, Scott; Paulsen, Vern

doi:10.1090/S0002-9939-1989-0972236-8

A note on joint hyponormality

Authors: Scott McCullough and Vern Paulsen
Journal: Proc. Amer. Math. Soc. 107 (1989), 187-195
MSC: Primary 47B20
DOI: https://doi.org/10.1090/S0002-9939-1989-0972236-8
MathSciNet review: 972236
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Abstract: We describe certain cones of polynomials in two variables naturally associated to the class(es) of operators for which the tuple $(T,{T^2}, \ldots ,{T^n})$ is jointly (weakly) hyponormal. As an application we give an example of an operator such that the tuple $(T,{T^2})$ is jointly but not weakly hyponormal. Further, we show that there exists a polynomially hyponormal operator which is not subnormal if and only if there exists a weighted shift with the same property.

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