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On the spectrum of multivariable weighted composition operators

Authors:

Isabelle Chalendar Antoine Flattot Nadine Guillotin-Plantard

Affiliation:

(1) Université Claude Bernard, Lyon 1, 43, bld du 11 novembre 1918, F-69622 Villeurbanne, France

Abstract:

In this paper we study the point spectrum of the operator

$T_{w,tau} : L^p([0, 1]^d) rightarrow L^p([0, 1]^d), f mapsto w f circ tau$

where d ≥ 1, 1 ≤ p ≤ ∞([0, 1]^d) and τ is an irrational rotation on [0, 1]^d. For a particular class of weights w, the point spectrum of T _w,τ is shown to be empty, generalizing Davie’s result [3], who considered the case p = 2, d = 1. Received: 1 June 2007, Revised: 16 October 2007

Keywords:

KeywordHeading" >Mathematics Subject Classification (2000). Primary 47A75 Secondary 47A15, 47A35

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