Invariant subspaces for a class of complete Pick kernels

Jury, Michael

doi:10.1090/S0002-9939-05-07940-2

Invariant subspaces for a class of complete Pick kernels
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by Michael T. Jury PDF

Proc. Amer. Math. Soc. 133 (2005), 3589-3596 Request permission

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.

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