Digital Commons Network^™

The Backward Shift On The Space Of Chauchy Transforms, William T. Ross, Joseph A. Cima, Alec L. Matheson

Department of Math & Statistics Faculty Publications

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)). We examine this question when the space of Cauchy transforms is endowed with both the norm and weak* topologies.