A functional model for pure Γ-contractions

Bhattacharyya, Tirthankar ; Pal, Sourav (2014) A functional model for pure Γ-contractions Journal of Operator Theory, 71 (2). pp. 327-339. ISSN 0379-4024

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Official URL: http://www.mathjournals.org/jot/2014-071-002/2014-...

Related URL: http://dx.doi.org/10.7900/jot.2012mar21.1946


A pair of commuting operators (S,P) defined on a Hilbert space H for which the closed symmetrized bidisc Γ = {(z1+z2, z1z2):|z1| ≤ 1,|z2| ≤ 1} ⊆ C2 is a spectral set is called a Γ-contraction in the literature. A Γ-contraction (S,P) is said to be pure if P is a pure contraction, i.e., P*n → 0 strongly as n → ∞. Here we construct a functional model and produce a set of unitary invariants for a pure Γ-contraction. The key ingredient in these constructions is an operator, which is the unique solution of the operator equation S-S*P=DpXDp, where X ϵ B(Dp),and is called the fundamental operator of the Γ-contraction (S,P). We also discuss some important properties of the fundamental operator.

Item Type:Article
Source:Copyright of this article belongs to Theta Foundation.
Keywords:Symmetrized Bidisc; Fundamental Operator; Functional Model; Unitary Invariants
ID Code:99722
Deposited On:27 Nov 2016 12:50
Last Modified:27 Nov 2016 12:50

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