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

 

Projective modules and Hilbert spaces
with a Nevanlinna-Pick kernel


Authors: Robert S. Clancy and Scott McCullough
Journal: Proc. Amer. Math. Soc. 126 (1998), 3299-3305
MSC (1991): Primary 47A20; Secondary 46E22
MathSciNet review: 1473659
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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.


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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
Email: sam@math.ufl.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04624-3
PII: S 0002-9939(98)04624-3
Received by editor(s): January 17, 1997
Received by editor(s) in revised form: March 28, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society