Projective modules and Hilbert spaces with a Nevanlinna-Pick kernel
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- by Robert S. Clancy and Scott McCullough PDF
- Proc. Amer. Math. Soc. 126 (1998), 3299-3305 Request permission
Abstract:
In this paper we solve a mapping problem for a particular class of Hilbert modules over an algebra multipliers of a diagonal Nevanlinna-Pick (NP) kernel. In this case, the regular representation provides a multiplier norm which induces the topology on the algebra. In particular, we show that, in an appropriate category, a certain class of Hilbert modules are projective. In addition, we establish a commutant lifting theorem for diagonal NP kernels.References
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Additional Information
- Robert S. Clancy
- Affiliation: Department of Mathematics, 358 Little Hall, University of Florida, Gainesville, Florida 32611
- Email: rsc@math.ufl.edu
- Scott McCullough
- Affiliation: Department of Mathematics, 358 Little Hall, University of Florida, Gainesville, Florida 32611
- MR Author ID: 220198
- Email: sam@math.ufl.edu
- Received by editor(s): January 17, 1997
- Received by editor(s) in revised form: March 28, 1997
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 3299-3305
- MSC (1991): Primary 47A20; Secondary 46E22
- DOI: https://doi.org/10.1090/S0002-9939-98-04624-3
- MathSciNet review: 1473659