Reconstruction of the Berger measure when the core is of tensor form

Abstract

Let ${\mathfrak{H}}_0$ denote the class of commuting pairs of subnormal operators on Hilbert space, and let $\mathcal{TC}:=\{\mathbf{T}\in \mathfrak{% H}_{0}:c(\mathbf{T)}$ is of tensor form$\}$, where $c(\mathbf{T})$ is the core of $\mathbf{T}$. We obtain a concrete necessary and sufficient condition for the subnormality of $\mathbf{T}\equiv (T_1,T_2)\in \mathcal{T}\mathcal{C}$ in terms of $c(\mathbf{T})$, the marginal measures of $T_1$ and $T_2$, and the weight ${\alpha }_{01}$.

Bibl. Rev. Mat. Iberoamericana, to appear; 11 pp. in preprint form