Mappings preserving spectra of products of matrices

Authors:
Jor-Ting Chan, Chi-Kwong Li and Nung-Sing Sze

Journal:
Proc. Amer. Math. Soc. **135** (2007), 977-986

MSC (2000):
Primary 15A04, 15A18

Published electronically:
October 4, 2006

MathSciNet review:
2262897

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be the set of complex matrices, and for every , let denote the spectrum of . For various types of products on , it is shown that a mapping satisfying for all has the form

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Additional Information

**Jor-Ting Chan**

Affiliation:
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong

Email:
jtchan@hku.hk

**Chi-Kwong Li**

Affiliation:
Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187-8795

Email:
ckli@math.wm.edu

**Nung-Sing Sze**

Affiliation:
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong.

Address at time of publication:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269-3009

Email:
NungSingSze@graduate.hku.hk

DOI:
https://doi.org/10.1090/S0002-9939-06-08568-6

Keywords:
Eigenvalue,
spectrum,
preserve

Received by editor(s):
April 7, 2005

Received by editor(s) in revised form:
November 10, 2005

Published electronically:
October 4, 2006

Additional Notes:
This research was partially supported by Hong Kong RCG CERG grant HKU 7007/03P. The second author was also supported by a USA NSF grant.

The second author is also an honorary professor of the Heilongjiang University, and an honorary professor of the University of Hong Kong.

Dedicated:
Dedicated to Professor Ahmed Sourour on the occasion of his sixtieth birthday.

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2006
American Mathematical Society