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The spectral mapping property for p–multiplier operators on compact abelian groups

Part of: Abstract harmonic analysis General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Werner J. Ricker
Werner J. Ricker
Affiliation:
Math.-Geogr. FakultätKatholische Universität Eichstätt-IngolstadtD-85072 EichstättGermany e-mail: [email protected]
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Abstract

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Let G be a compact abelian group and 1< p < ∞. It is known that the spectrum σ (Tψ) of a Fourier p–multiplier operator Tψ acting in Lp(G), may fail to coincide with its natural spectrum ψ(Г) if p ≠ 2; here Γ is the dual group to G and the bar denotes closure in C. Criteria are presented, based on geometric, topological and/or algebraic properties of the compact set σ(Tψ), which are sufficient to ensure that the equality σ(Tψ) = ψ(Г)holds.

MSC classification

Secondary: 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 47A10: Spectrum, resolvent
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 78 , Issue 3 , June 2005 , pp. 423 - 428
Copyright
Copyright © Australian Mathematical Society 2005

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