Operator positivity and analytic models of commuting tuples of operators

• Autorzy: Monojit Bhattacharjee , Jaydeb Sarkar
• Języki publikacji: 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.

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 47A80: Tensor products of operators
• 47A45: Canonical models for contractions and nonselfadjoint operators
• 47A13: Several-variable operator theory (spectral, Fredholm, etc.)
• 47B32: Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
• 47A15: Invariant subspaces
• 47A20: Dilations, extensions, compressions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2016
• Tom: 232
• Numer: 2
• Strony: 155-171

Daty

wydano

2016

Twórcy

autor

Monojit Bhattacharjee

• Indian Institute of Science, Department of Mathematics, Bangalore, 560012, India

autor

Jaydeb Sarkar

• Indian Statistical Institute, Statistics and Mathematics Unit, 8th Mile, Mysore Road, Bangalore, 560059, India

Identyfikatory

DOI

10.4064/sm8437-2-2016