Isometries for Ky Fan norms between matrix spaces

Authors:
Chi-Kwong Li, Yiu-Tung Poon and Nung-Sing Sze

Journal:
Proc. Amer. Math. Soc. **133** (2005), 369-377

MSC (2000):
Primary 15A04, 15A60

DOI:
https://doi.org/10.1090/S0002-9939-04-07510-0

Published electronically:
August 26, 2004

MathSciNet review:
2093057

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We characterize linear maps between different rectangular matrix spaces preserving Ky Fan norms.

**1.**R. Bhatia,*Matrix Analysis*, Springer-Verlag, New York, 1997. MR**98i:15003****2.**W. S. Cheung and C. K. Li,*Linear maps transforming the unitary group*, Bulletin Canad. Math. Soc. 46 (2003), 54-58. MR**2003m:15007****3.**W. S. Cheung, C. K. Li and Y. T. Poon,*Isometries between matrix algebras*, to appear in J. Australian Math. Soc. pdf file available at http://www.resnet.wm.edu/ cklixx/poon-7.pdf.**4.**R. Grone and M. Marcus,*Isometries of matrix algebras*, J. Algebra 47 (1977), 180-189. MR**56:3039****5.**R. V. Kadison,*Isometries of operator algebras*, Ann. of Math. (2) 54 (1951), 325-338. MR**13:256a****6.**C. K. Li,*Matrices with some extremal properties*, Linear Algebra Appl. 101 (1988), 255-267. MR**89c:15025****7.**C. K. Li, L. Rodman, and P. Semrl,*Linear transformations between matrix spaces that map one rank specific set into another*, Linear Algebra Appl. 357 (2002), 197-208. MR**2003i:15002****8.**C. K. Li, P. Semrl, and A. R. Sourour,*Isometries for Ky-Fan norms on block triangular matrix algebras*, Archiv Math. 81 (2003), 175-181.

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Additional Information

**Chi-Kwong Li**

Affiliation:
Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795

Email:
ckli@math.wm.edu

**Yiu-Tung Poon**

Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011 – and – Department of Mathematics, HKIEd, Hong Kong

Email:
ytpoon@ied.edu.hk

**Nung-Sing Sze**

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

Email:
math2000@graduate.hku.hk

DOI:
https://doi.org/10.1090/S0002-9939-04-07510-0

Keywords:
Isometry,
matrices,
linear maps

Received by editor(s):
July 8, 2003

Received by editor(s) in revised form:
August 26, 2003

Published electronically:
August 26, 2004

Additional Notes:
The first author’s research was partially supported by NSF

The third author thanks Dr. Jor-Ting Chan for his guidance and encouragement

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2004
American Mathematical Society