A Product Formula for Homogeneous Characteristic Functions
نویسندگان
چکیده
A bounded linear operator T on a Hilbert space is said to be homogeneous if $$\varphi (T)$$ unitarily equivalent for all $$ in the group Möb of bi-holomorphic automorphisms unit disc. projective unitary representation $$\sigma associated with an (T)= \sigma (\varphi )^* )$$ Möb. In this paper, we develop Möbius equivariant version Sz.-Nagy–Foias model theory completely non-unitary (cnu) contractions. As application, prove that cnu contraction (projective unitary) , then there unique $${\hat{\sigma }}$$ extending minimal dilation T. The given terms by formula $$\begin{aligned} {\hat{\sigma }} = (\pi \otimes D_1^+) \oplus _*\otimes D_1^-), \end{aligned}$$ where $$D_1^\pm are two representations (one holomorphic and other anti-holomorphic) living Hardy $$H^2({\mathbb {D}})$$ $$\pi \pi _*$$ defect spaces defined explicitly . Moreover, has only its characteristic function $$\theta _T$$ product form _T(z) _*(\varphi _z)^* \theta _T(0) _z),$$ $$z\in {\mathbb {D}}$$ _z$$ involution mapping z 0. We obtain concrete realization large subclass contractions from Cowen–Douglas class.
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ژورنال
عنوان ژورنال: Integral Equations and Operator Theory
سال: 2023
ISSN: ['0378-620X', '1420-8989']
DOI: https://doi.org/10.1007/s00020-023-02730-x