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Generalized numerical ranges, joint positive definiteness and multiple eigenvalues

Author: Yiu Tung Poon
Journal: Proc. Amer. Math. Soc. 125 (1997), 1625-1634
MSC (1991): Primary 15A60; Secondary 47A12
MathSciNet review: 1372044
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Abstract: We prove a convexity theorem on a generalized numerical range that combines and generalizes the following results: 1) Friedland and Loewy's result on the existence of a nonzero matrix with multiple first eigenvalue in subspaces of hermitian matrices, 2) Bohnenblust's result on joint positive definiteness of hermitian matrices, 3) the Toeplitz-Hausdorff Theorem on the convexity of the classical numerical range and its various generalizations by Au-Yeung, Berger, Brickman, Halmos, Poon, Tsing and Westwick.

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Additional Information

Yiu Tung Poon

Keywords: Generalized numerical range, convexity, joint positive definiteness, multiple eigenvalue
Received by editor(s): September 22, 1995
Received by editor(s) in revised form: January 4, 1996
Additional Notes: The author wants to thank the referee for some helpful comments and suggestions.
Dedicated: Dedicated to Professor Yik Hoi Au-Yeung
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

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