The homogeneous shifts

Bagchi, Bhaskar ; Misra, Gadadhar (2003) The homogeneous shifts Journal of Functional Analysis, 204 (2). pp. 293-319. ISSN 0022-1236

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00221...

Related URL: http://dx.doi.org/10.1016/S0022-1236(02)00088-5

Abstract

A bounded linear operator Tau on a complex Hilbert space is called homogeneous if the spectrum of Tau is contained in the closed unit disc and all bi-holomorphic automorphisms of this disc lift to automorphisms of the operator modulo unitary equivalence. We prove that all the irreducible homogeneous operators are block shifts. Therefore, as a first step in classifying all of them, it is natural to begin with the homogeneous scalar shifts. In this paper we determine all the homogeneous (scalar) weighted shifts. They consist of the unweighted bilateral shift, two one-parameter families of unilateral shifts (adjoints of each other), a one-parameter family of bilateral shifts and a two-parameter family of bilateral shifts. This classification is obtained by a careful analysis of the possibilities for the projective representation of the Möbius group associated with an irreducible homogeneous shift.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:990
Deposited On:25 Sep 2010 06:34
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