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Projective modules and Hilbert spaces with a Nevanlinna-Pick kernel
Author(s):
Robert
S.
Clancy;
Scott
McCullough
Journal:
Proc. Amer. Math. Soc.
126
(1998),
3299-3305.
MSC (1991):
Primary 47A20;
Secondary 46E22
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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:
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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