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.
Copyright © American Mathematical Society. This article first appeared in Proceedings of the American Mathematical Society 132:3 (2004), 745-754.
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Ross, William T., Joseph A. Cima, and Alec L. Matheson. "The Backward Shift on the Space of Cauchy Transforms." Proceedings of the American Mathematical Society 132, no. 3 (2004): 745-754.