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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A spectral commutant lifting theorem


Authors: Hari Bercovici, Ciprian Foias and Allen Tannenbaum
Journal: Trans. Amer. Math. Soc. 325 (1991), 741-763
MSC: Primary 47A20; Secondary 30E05, 93B28
MathSciNet review: 1000144
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Abstract: The commutant lifting theorem of [24] may be regarded as a very general interpolation theorem from which a number of classical interpolation results may be deduced. In this paper we prove a spectral version of the commutant lifting theorem in which one bounds the spectral radius of the interpolant and not the norm. We relate this to a spectral analogue of classical matricial Nevanlinna-Pick interpolation.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1000144-9
PII: S 0002-9947(1991)1000144-9
Keywords: Commutant lifting theorem, dilation theory, spectral radius, interpolation theory
Article copyright: © Copyright 1991 American Mathematical Society