A note on joint hyponormality

McCullough, Scott; Paulsen, Vern

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

A note on joint hyponormality
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by Scott McCullough and Vern Paulsen

Proc. Amer. Math. Soc. 107 (1989), 187-195

DOI: https://doi.org/10.1090/S0002-9939-1989-0972236-8

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Abstract:

We describe certain cones of polynomials in two variables naturally associated to the class(es) of operators $T$ for which the tuple $(T,{T^2}, \ldots ,{T^n})$ is jointly (weakly) hyponormal. As an application we give an example of an operator $T$ 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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