Year: 1989
Type: article
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.
Authors: Scott McCullough, Vern Paulsen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W2051939980