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A Helson-Lowdenslager-deBranges Theorem in $L^2$


Authors: Vern I. Paulsen and Dinesh Singh
Journal: Proc. Amer. Math. Soc. 129 (2001), 1097-1103
MSC (1991): Primary 47A15
DOI: https://doi.org/10.1090/S0002-9939-00-05716-6
Published electronically: October 31, 2000
MathSciNet review: 1814147
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Abstract | References | Similar Articles | Additional Information

Abstract:

This paper presents a generalization of the invariant subspace theorem of Helson and Lowdenslager along the lines of de Branges' generalization of Beurling's theorem.


References [Enhancements On Off] (What's this?)

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  • 2. H. Helson, Harmonic Analysis, Hindustan Book Agency (1995). MR 96m:42001
  • 3. H. Helson and D. Lowdenslager, Invariant subspaces, Proc. Int. Symp. Linear Spaces, Jerusalem, (1960) 251-262, Macmillan. MR 28:487
  • 4. K. Hoffman, Banach Spaces of Analytic Functions, Prentice Hall, (1962). MR 24:A2844
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  • 6. D. Sarason, Shift invariant spaces from the Brangesian point of view. The Bieberbach Conjecture-Proceedings of the Symposium of the Occasion of the Proof, Amer. Math. Soc. (1986). MR 88d:47014a
  • 7. D. Sarason, Sub-Hardy Hilbert Spaces in the Unit Disk, John Wiley and Sons (1994). MR 96k:46039

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Additional Information

Vern I. Paulsen
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204-3476
Email: vern@math.uh.edu

Dinesh Singh
Affiliation: Department of Mathematics, University of Delhi, Delhi-110007, India
Email: dinesh_singh@hotmail.com

DOI: https://doi.org/10.1090/S0002-9939-00-05716-6
Keywords: Helson-Lowdenslager theorem, de Branges' theorem, contractively contained
Received by editor(s): June 30, 1999
Published electronically: October 31, 2000
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society

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