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A characterization of multiplication operators on reproducing kernel Hilbert spaces

By Christoph Barbian

Abstract

In this note, we prove that an operator between reproducing kernel Hilbert spaces is a multiplication operator if and only if it leaves invariant zero sets. To be more precise, it is shown that an operator T between reproducing kernel Hilbert spaces is a multiplication operator if and only if (Tf)(z)=0 holds for all f and z satisfying f(z)=0. As possible applications, we deduce a general reflexivity result for multiplier algebras, and furthermore prove fully vector-valued generalizations of mulitplier lifting results of Beatrous and Burbea

Topics: Mathematics
Publisher: Fakultät 6 - Naturwissenschaftlich-Technische Fakultät I. Fachrichtung 6.1 - Mathematik
Year: 2008
OAI identifier: oai:scidok.sulb.uni-saarland.de:4738

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