Proceedings of the American Mathematical Society

Author(s): V. V. Peller
Journal: Proc. Amer. Math. Soc. 137 (2009), 205-210.
MSC (2000): Primary 47B35, 46E40, 30D55, 30E10
Posted: August 4, 2008
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Abstract: We study the question of the existence of a dual extremal function for a bounded matrix function on the unit circle in connection with the problem of approximation by analytic matrix functions. We characterize the class of matrix functions, for which a dual extremal function exists in terms of the existence of a maximizing vector of the corresponding Hankel operator and in terms of certain special factorizations that involve thematic matrix functions.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B35, 46E40, 30D55, 30E10

V. V. Peller
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

DOI: 10.1090/S0002-9939-08-09623-8
PII: S 0002-9939(08)09623-8
Keywords: Best approximation, badly approximable matrix functions, dual extremal function, Hankel operator, maximizing vector
Received by editor(s): December 18, 2007
Posted: August 4, 2008
Additional Notes: The author is partially supported by NSF grant DMS 0700995
Communicated by: Michael T. Lacey
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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