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 - Saarländische Universitäts- und Landesbibliothek
AD - Postfach 151141, 66041 Saarbrücken
UR - http://scidok.sulb.uni-saarland.de/volltexte/2012/4738
ER -