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Ideals of the Fourier algebra, supports and harmonic operators

Published online by Cambridge University Press:  02 May 2016

M. ANOUSSIS ,
A. KATAVOLOS  and
I. G. TODOROV
M. ANOUSSIS
Affiliation:
Department of Mathematics, University of the Aegean, Samos 83 200, Greece. e-mail: mano@aegean.gr
A. KATAVOLOS
Affiliation:
Department of Mathematics, University of Athens, Athens 157 84, Greece. e-mail: akatavol@math.uoa.gr
I. G. TODOROV
Affiliation:
Pure Mathematics Research Centre, Queen's University Belfast, Belfast BT7 1NN. e-mail: i.todorov@qub.ac.uk
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Abstract

We examine the common null spaces of families of Herz–Schur multipliers and apply our results to study jointly harmonic operators and their relation with jointly harmonic functionals. We show how an annihilation formula obtained in [1] can be used to give a short proof as well as a generalisation of a result of Neufang and Runde concerning harmonic operators with respect to a normalised positive definite function. We compare the two notions of support of an operator that have been studied in the literature and show how one can be expressed in terms of the other.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 161 , Issue 2 , September 2016 , pp. 223 - 235
Copyright
Copyright © Cambridge Philosophical Society 2016 

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