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

 

Linear operators preserving the numerical radius of matrices


Author: Chi-Kwong Li
Journal: Proc. Amer. Math. Soc. 99 (1987), 601-608
MSC: Primary 15A04; Secondary 15A60
MathSciNet review: 877024
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Abstract: In this note we characterize all the linear operators on the linear space of $ n \times n$ complex matrices which preserve the numerical radius and all the linear operators on the real linear space of $ n \times n$ Hermitian matrices which preserve the numerical radius. From our results, we easily deduce V. J. Pellegrini's characterization of all linear operators that preserve the numerical ranges of matrices and the result of Marcus and Moyls concerning the linear operators that preserve the eigenvalues of Hermitian matrices.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0877024-7
PII: S 0002-9939(1987)0877024-7
Article copyright: © Copyright 1987 American Mathematical Society