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

 

Invariant subspaces for a class of complete Pick kernels


Author: Michael T. Jury
Journal: Proc. Amer. Math. Soc. 133 (2005), 3589-3596
MSC (2000): Primary 47B32; Secondary 47A15, 47A16
Published electronically: June 28, 2005
MathSciNet review: 2163594
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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 Szego 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.


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Additional Information

Michael T. Jury
Affiliation: Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, Indiana 47907-2067
Email: jury@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07940-2
PII: S 0002-9939(05)07940-2
Keywords: Pick kernel, invariant space, cyclic vector
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.