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Invariant subspaces for a class of complete Pick kernels
Author(s):
Michael
T.
Jury
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3589-3596.
MSC (2000):
Primary 47B32;
Secondary 47A15, 47A16
Posted:
June 28, 2005
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Abstract:
Motivated by the work of McCullough and Trent, we investigate the  -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  -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:
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
Posted:
June 28, 2005
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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