On a conjecture of ridge
Author:
TinYau Tam
Journal:
Proc. Amer. Math. Soc. 125 (1997), 35813592
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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 [C]
 J. B. Conway, The Theory of Subnormal Operators, Math. Surveys and Monographs, Vol. 36, Amer. Math. Soc., Providence, R.I., 1991. MR 92h:47026
 [CL]
 M. D. Choi and C.K. Li, Numerical ranges of the powers of an operator, preprint.
 [Ch]
 T. R. Chow, The spectral radius of a direct integral of operators, Math. Ann. 188 (1970), 285303.
 [H]
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 [HJ]
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 M. Marcus and B. N. Shure, The numerical range of certain 0,1matrices, Linear and Multilinear Algebra, 7 (1979), 111120. MR 80c:15015
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 W. Ridge, Approximate point spectrum of a weighted shift, Trans. Amer. Math. Soc., 147 (1970), 349356. MR 40:7843
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Additional Information
TinYau Tam
Affiliation:
Department of Mathematics, Auburn University, Alabama 368495310
Email:
tamtiny@mail.auburn.edu
DOI:
http://dx.doi.org/10.1090/S0002993997040355
PII:
S 00029939(97)040355
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 MiniConference in Hong Kong, June, 1995.
Communicated by:
Palle E. T. Jorgensen
Article copyright:
© Copyright 1997
American Mathematical Society
