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

Curto, Raul E.; Lee, Sang Hoon; Yoon, Jasang

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

Authors

Curto, Raul E.

Lee, Sang Hoon

Yoon, Jasang

Description

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 $\mathbf{T}\equiv (T_{1},T_{2})\in \mathcal{TC}$ 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 form