TY  - GEN
T1  - A characterization of multiplication operators on reproducing kernel Hilbert spaces
A1  - Barbian,Christoph
Y1  - 2012/03/23
N2  - 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.
CY  - Saarbrücken
PB  - Universitäts- und Landesbibliothek
AD  - Postfach 151141, 66041 Saarbrücken
UR  - http://scidok.sulb.uni-saarland.de/volltexte/2012/4738
ER  -