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 | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-97-04035-5

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