Approximation properties for multiplier algebras of reproducing kernel Hilbert spaces

Abstract

In this note, it is proved that multiplier algebras of analytic reproducing kernel Hilbert spaces which are compatible with the action of the torus group possess Kraus’ completely contractive approximation property (CCAP) and, consequently, have the Property S_{\sigma}. Our results apply in particular to the usual reproducing kernel Hilbert spaces on bounded symmetric domains.