The backward shift on the space of Cauchy transforms

Abstract

This note examines the subspaces of the space of Cauchy transforms of measures on the unit circle that are invariant under the backward shift operator f → z − 1 ( f − f ( 0 ) ) f \to z^{-1}(f - f(0)) . We examine this question when the space of Cauchy transforms is endowed with both the norm and weak ∗ {}^* topologies.