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ORDER PRESERVING MAPS ON HERMITIAN MATRICES

Part of: Special matrices

Published online by Cambridge University Press:  07 June 2013

PETER ŠEMRL  and
AHMED RAMZI SOUROUR
PETER ŠEMRL*
Affiliation:
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000, Slovenia
AHMED RAMZI SOUROUR
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8P 5C2 email [email protected]
*
✉[email protected]
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Abstract

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We prove that a continuous map $\phi $ defined on the set of all $n\times n$ Hermitian matrices preserving order in both directions is up to a translation a congruence transformation or a congruence transformation composed with the transposition.

Keywords

order preserving mapHermitian matrix

MSC classification

Secondary: 15B48: Positive matrices and their generalizations; cones of matrices 15B57: Hermitian, skew-Hermitian, and related matrices
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 95 , Issue 1 , August 2013 , pp. 129 - 132
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Fulton, W., Algebraic Topology: A First Course, Graduate Texts in Mathematics, 153 (Springer, New York, NY, 1995).CrossRefGoogle Scholar
Huang, W.-l. and Šemrl, P., ‘Adjacency preserving maps on Hermitian matrices’, Canad. J. Math. 60 (2008), 1050–1066.CrossRefGoogle Scholar
Molnár, L., ‘Order-automorphisms of the set of bounded observables’, J. Math. Phys. 42 (2001), 5904–5909.CrossRefGoogle Scholar
Molnár, L., Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces, Lecture Notes in Mathematics, 1895 (Springer, Berlin, 2007).Google Scholar
Šemrl, P., ‘Comparability preserving maps on bounded observables’, Integral Equations Operator Theory 62 (2008), 441–454.CrossRefGoogle Scholar