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

DOI:
https://doi.org/10.1090/S0002-9939-97-03781-7

MathSciNet review:
1372044

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Abstract | References | Similar Articles | Additional Information

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**

Email:
ytpoon@iastate.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03781-7

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