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

 

Relaxed commutant lifting: Existence of a unique solution


Author: S. ter Horst
Journal: Proc. Amer. Math. Soc. 137 (2009), 2697-2707
MSC (2000): Primary 47A20, 47A56, 47A57
Published electronically: February 4, 2009
MathSciNet review: 2497482
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Abstract: In this paper we present necessary and sufficient conditions for the existence of a unique solution to the relaxed commutant lifting problem. The obtained conditions are more complicated than those for the classical commutant lifting setting, and earlier obtained sufficient conditions turn out not to be necessary conditions. It is also shown that these conditions simplify in certain special cases.


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Additional Information

S. ter Horst
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123
Email: terhorst@math.vt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09813-X
PII: S 0002-9939(09)09813-X
Keywords: Commutant lifting, unique solution, linear fractional maps
Received by editor(s): March 3, 2008
Received by editor(s) in revised form: October 20, 2008
Published electronically: February 4, 2009
Communicated by: Marius Junge
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.