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

## Abstract

A pair of commuting operators (S,P) defined on a Hilbert space H for which the closed symmetrized bidisc Γ = {(z_{1}+z_{2}, z_{1}z_{2}):|z_{1}| ≤ 1,|z_{2}| ≤ 1} ⊆ C^{2} 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=D_{p}XD_{p}, where X ϵ B(D_{p}),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 |
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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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