Journal of Operator Theory

Volume 49, Issue 2, Spring 2003 pp. 295-310.

Fuglede's theorem, the bicommutant theorem and $p$-multiplier operators for the circle

Authors: Gerd Mockenhaupt (1) and Werner J. Ricker (2)
Author institution: (1) School of Mathematics, Georgia Institue of Technology, Atlanta, GA 30332-0160, USA
(2) Mathematisch-Geographisch e Fakultaet, Katholische Universitaet Eichstaett, D-85072 Eichstaett, Germany

Summary: Two classical results concerning normal operators in a Hilbert space are the Fuglede commutativity theorem and von Neumann's bicommutant theorem. Analogues of these results are established for Fourier multiplier operators acting in $L^p$-spaces of the circle group, for $1<p<\infty$. The arguments used are a combination of techniques coming from harmonic analysis, functional analysis and operator theory.

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