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A FUNCTIONAL MODEL FOR PURE Gamma-CONTRACTIONS

Bhattacharyya, Tirthankar and Pal, Sourav (2014) A FUNCTIONAL MODEL FOR PURE Gamma-CONTRACTIONS. In: JOURNAL OF OPERATOR THEORY, 71 (2). pp. 327-339.

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Official 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 Gamma = {(z(1) + z(2), z(1)z(2)) : vertical bar z(1)vertical bar <= 1, vertical bar z(2)vertical bar <= 1} subset of C-2 is a spectral set is called a Gamma-contraction in the literature. A Gamma-contraction (S, P) is said to be pure if P is a pure contraction, i.e., P*(n) -> 0 strongly as n -> infinity Here we construct a functional model and produce a set of unitary invariants for a pure Gamma-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 is an element of B(D-p), and is called the fundamental operator of the Gamma-contraction (S, P). We also discuss some important properties of the fundamental operator.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the THETA FOUNDATION, C/O INST MATHEMATICS, PO BOX 1-764, BUCHAREST 70700, ROMANIA
Keywords: Symmetrized bidisc; fundamental operator; functional model; unitary invariants
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 06 Sep 2014 06:26
Last Modified: 06 Sep 2014 06:26
URI: http://eprints.iisc.ac.in/id/eprint/49773

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