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

 

On a conjecture of ridge


Author: Tin-Yau Tam
Journal: Proc. Amer. Math. Soc. 125 (1997), 3581-3592
MSC (1991): Primary 47A12, 47B20
MathSciNet review: 1415372
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Abstract: The conjecture of Ridge on the numerical range of a shift of periodic weights is resolved in the affirmative, i.e., if the weights are nonzero, the numerical range of the corresponding shift is an open disc centered at the origin. The radius of the disc can be expressed as the Perron root of a nonnegative irreducible symmetric matrix. Some related results are obtained.


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Additional Information

Tin-Yau Tam
Affiliation: Department of Mathematics, Auburn University, Alabama 36849-5310
Email: tamtiny@mail.auburn.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04035-5
PII: S 0002-9939(97)04035-5
Keywords: Weighted shift, numerical range
Received by editor(s): February 22, 1996
Received by editor(s) in revised form: July 3, 1996
Additional Notes: Some results of the paper have been presented in the Third Matrix Theory Mini-Conference in Hong Kong, June, 1995.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society