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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The backward shift on the space of Cauchy transforms


Authors: Joseph A. Cima, Alec Matheson and William T. Ross
Journal: Proc. Amer. Math. Soc. 132 (2004), 745-754
MSC (2000): Primary 46E15, 47A15; Secondary 47A16
Published electronically: July 16, 2003
MathSciNet review: 2019951
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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 $f \to z^{-1}(f - f(0))$. We examine this question when the space of Cauchy transforms is endowed with both the norm and weak${}^*$ topologies.


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Additional Information

Joseph A. Cima
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599
Email: cima@math.unc.edu

Alec Matheson
Affiliation: Department of Mathematics, Lamar University, Beaumont, Texas 77710
Email: matheson@math.lamar.edu

William T. Ross
Affiliation: Department of Mathematics and Computer Science, University of Richmond, Richmond, Virginia 23173
Email: wross@richmond.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07103-X
PII: S 0002-9939(03)07103-X
Keywords: Cauchy transforms, backward shift operator
Received by editor(s): October 10, 2002
Received by editor(s) in revised form: October 21, 2002
Published electronically: July 16, 2003
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society