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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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