An F. and M. Riesz Theorem for strong H2-functions on the unit circle

Abstract

An F. and M. Riesz Theorem states that if f,g∈H2 are such that fg=0 a.e. on the unit circle T then either f=0 a.e. on T or g=0 a.e. on T. In this paper we establish an extension of the F. and M. Riesz Theorem for (operator-valued) strong H2-functions on the unit circle.