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• # Artykuł - szczegóły

## Studia Mathematica

2016 | 232 | 2 | 155-171

## Operator positivity and analytic models of commuting tuples of operators

EN

### Abstrakty

EN
We study analytic models of operators of class $C_{·0}$ with natural positivity assumptions. In particular, we prove that for an m-hypercontraction $T ∈ C_{·0}$ on a Hilbert space 𝓗, there exist Hilbert spaces 𝓔 and 𝓔⁎ and a partially isometric multiplier θ ∈ ℳ (H²(𝓔),A²ₘ(𝓔⁎)) such that
$𝓗 ≅ 𝓠_{θ} = A²ₘ(𝓔⁎) ⊖ θH²(𝓔)$ and $T ≅ P_{𝓠_{θ}} M_{z}|_{𝓠_{θ}}$,
where A²ₘ(𝓔⁎) is the 𝓔⁎-valued weighted Bergman space and H²(𝓔) is the 𝓔-valued Hardy space over the unit disc 𝔻. We then proceed to study analytic models for doubly commuting n-tuples of operators and investigate their applications to joint shift co-invariant subspaces of reproducing kernel Hilbert spaces over the polydisc. In particular, we completely analyze doubly commuting quotient modules of a large class of reproducing kernel Hilbert modules, in the sense of Arazy and Engliš, over the unit polydisc 𝔻ⁿ.

155-171

wydano
2016

### Twórcy

• Indian Institute of Science, Department of Mathematics, Bangalore, 560012, India
autor
• Indian Statistical Institute, Statistics and Mathematics Unit, 8th Mile, Mysore Road, Bangalore, 560059, India