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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140490Let $\mathfrak{H}_{0}$ 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 $\mathbf{T}\equiv (T_{1},T_{2})\in \mathcal{TC}$ in terms of $c(\mathbf{T})$, the marginal measures of $T_{1}$ and $T_{2}$, and the weight $α_{01}$.Bibl. Rev. Mat. Iberoamericana, to appear; 11 pp. in preprint formFunctional Analysis47B20, 47B37, 47A13, 28A50 (Primary) 44A60, 47-04, 47A20 (Secondary)Reconstruction of the Berger measure when the core is of tensor formtext