A note on tetrablock contractions

Sau, Haripada (2015) A note on tetrablock contractions. In: NEW YORK JOURNAL OF MATHEMATICS, 21 . pp. 1347-1369.

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Abstract

A commuting triple of operators (A, B, P) on a Hilbert space H is called a tetrablock contraction if the closure of the set E = {(a(11),a(22),detA) : A = GRAPHICS] with parallel to A parallel to <1} is a spectral set. In this paper, we construct a functional model and produce a set of complete unitary invariants for a pure tetrablock contraction. In this construction, the fundamental operators, which are the unique solutions of the operator equations A - B* P = DPX1DP and B - A* P = DPX2DP where X-1, X-2 is an element of B(D-P) play a pivotal role. As a result of the functional model, we show that every pure tetrablock isometry (A, B, P) on an abstract Hilbert space H is unitarily equivalent to the tetrablock contraction (MG1*+G2z, MG2*+G1z, M-z) on H-DP*(2). (D), where G(1) and G(2) are the fundamental operators of (A*, B*, P*). We prove a Beurling Lax Halmos type theorem for a triple of operators (MF1*+F2z, MF2*+F1z, M-z), where epsilon is a Hilbert space and F-1, F-2 is an element of B(epsilon). We also deal with a natural example of tetrablock contraction on a functions space to find out its fundamental operators.

Item Type:	Journal Article
Publication:	NEW YORK JOURNAL OF MATHEMATICS
Publisher:	ELECTRONIC JOURNALS PROJECT
Additional Information:	Copy right for this article belongs to the ELECTRONIC JOURNALS PROJECT, UNIV ALBANY, DEPT MATHEMATICS & SCIENCE, ALBANY, NY 12222 USA
Keywords:	Tetrablock; tetrablock contraction; spectral set; Beurling-Lax-Halmos theorem; functional model; fundamental operator
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	14 Jan 2016 05:44
Last Modified:	14 Jan 2016 05:44
URI:	http://eprints.iisc.ac.in/id/eprint/53106

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