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A simple proof of necessity in the McCullough-Quiggin theorem


Author: Greg Knese
Journal: Proc. Amer. Math. Soc. 148 (2020), 3453-3456
MSC (2010): Primary 46E22, 47A57
DOI: https://doi.org/10.1090/proc/15061
Published electronically: April 9, 2020
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Abstract: A short and simple proof of necessity in the McCullough-Quiggin characterization of positive semi-definite kernels with the complete Pick property is presented.


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Greg Knese
Affiliation: Department of Mathematics and Statistics, Washington University in St. Louis, One Brookings Drive, St. Louis, Missouri 63130
Email: geknese@wustl.edu

DOI: https://doi.org/10.1090/proc/15061
Keywords: Complete Pick kernel, reproducing kernel Hilbert space
Received by editor(s): December 30, 2019
Published electronically: April 9, 2020
Additional Notes: The author was partially supported by NSF grant DMS-1900816
Communicated by: Stephan Ramon Garcia
Article copyright: © Copyright 2020 American Mathematical Society