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

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

2007-10-22

arxiv.org/abs/0710.3977v1

Mathematics

Functional Analysis

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

Scientific paper

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 $\alpha_{01}$.

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