Positive extensions of Schur multipliers

Abstract

We introduce partially defined Schur multipliers and obtain necessary and sufficient conditions for the existence of extensions to fully defined positive Schur multipliers, in terms of operator systems canonically associated with their domains. We use these results to study the problem of extending a positive definite function defined on a symmetric subset of a locally compact group to a positive definite function defined on the whole group.

References in corpus (1)

• Sets of multiplicity and closable multipliers on group algebras

Cited by in corpus (1)

• Reduced spectral synthesis and compact operator synthesis