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

Published electronically:
August 26, 2004

MathSciNet review:
2093057

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Abstract | References | Similar Articles | Additional Information

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

**1.**Rajendra Bhatia,*Matrix analysis*, Graduate Texts in Mathematics, vol. 169, Springer-Verlag, New York, 1997. MR**1477662****2.**Wai-Shun Cheung and Chi-Kwong Li,*Linear maps transforming the unitary group*, Canad. Math. Bull.**46**(2003), no. 1, 54–58. MR**1955612**, 10.4153/CMB-2003-005-8**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.**Robert Grone and Marvin Marcus,*Isometries of matrix algebras*, J. Algebra**47**(1977), no. 1, 180–189. MR**0444689****5.**Richard V. Kadison,*Isometries of operator algebras*, Ann. Of Math. (2)**54**(1951), 325–338. MR**0043392****6.**Chi-Kwong Li,*Matrices with some extremal properties*, Linear Algebra Appl.**101**(1988), 255–267. MR**941306**, 10.1016/0024-3795(88)90153-X**7.**Chi-Kwong Li, Leiba Rodman, and Peter Šemrl,*Linear transformations between matrix spaces that map one rank specific set into another*, Linear Algebra Appl.**357**(2002), 197–208. MR**1935234**, 10.1016/S0024-3795(02)00381-6**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:
http://dx.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