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Operator positivity and analytic models of commuting tuples of operators

100%

Bhattacharjee M., Sarkar J.

Studia Mathematica

2016

tom 232

nr 2

155-171

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.

Doubly commuting submodules of the Hardy module over polydiscs

81%

Sarkar J., Sasane A., Wick B.

Studia Mathematica

2013

tom 217

nr 2

179-192

In this note we establish a vector-valued version of Beurling's theorem (the Lax-Halmos theorem) for the polydisc. As an application of the main result, we provide necessary and sufficient conditions for the "weak" completion problem in $H^{∞}(𝔻ⁿ)$.

Ograniczanie wyników

2 Studia Mathematica

2 Sarkar J.

1 Bhattacharjee M.

1 Sasane A.

1 Wick B.

1 2016

1 2013

Wyniki wyszukiwania

Operator positivity and analytic models of commuting tuples of operators

Doubly commuting submodules of the Hardy module over polydiscs