Invariant subspaces for a class of complete Pick kernels
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- by Michael T. Jury PDF
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Abstract:
Motivated by the work of McCullough and Trent, we investigate the $z$–invariant subspaces of the Hilbert function spaces associated to the Szegő kernels on the open unit disk. In particular, we characterize those kernels for which the the $z$–invariant subspaces are hyperinvariant, and (partially) those for which the so-called BLH subspaces are cyclic, obtaining counterexamples to two questions posed by McCullough and Trent.References
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Additional Information
- Michael T. Jury
- Affiliation: Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, Indiana 47907-2067
- MR Author ID: 742791
- Email: jury@math.purdue.edu
- Received by editor(s): July 14, 2000
- Received by editor(s) in revised form: July 16, 2004
- Published electronically: June 28, 2005
- Communicated by: Joseph A. Ball
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 3589-3596
- MSC (2000): Primary 47B32; Secondary 47A15, 47A16
- DOI: https://doi.org/10.1090/S0002-9939-05-07940-2
- MathSciNet review: 2163594