Block matrix operators and weak hyponormalities (Q1049594)

The authors introduce a new model of a block matrix operator \(M(\alpha,\beta)\) induced by two sequences \(\alpha\) and \(\beta\) and characterize its \(p\)-hyponormality. The model is viewed as arising from the composition operator \(C_T\) on \(\ell^2_+:=L^2(\mathbb N_0)\) induced by a measurable transformation \(T\) on the set of nonnegative integers \(\mathbb N_0\) with point mass measure. The authors use composition operator techniques to characterize the \(p\)-hyponormality of \(M(\alpha,\beta)\) and apply their results to obtain examples of these operators showing that the \(p\)-hyponormal classes are distinct. This paper will be useful for the bridge theory of Hilbert space operators.