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

## 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 |
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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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