Geodesic
Maps on matrices that preserve the spectral radius distance
Studia Mathematica, Tome 134 (1999) no. 2, pp. 99-110

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let ϕ be a surjective map on the space of n×n complex matrices such that r(ϕ(A)-ϕ(B))=r(A-B) for all A,B, where r(X) is the spectral radius of X. We show that ϕ must be a composition of five types of maps: translation, multiplication by a scalar of modulus one, complex conjugation, taking transpose and (simultaneous) similarity. In particular, ϕ is real linear up to a translation.
DOI : 10.4064/sm-134-2-99-110

Rajendra Bhatia 1 ; Peter Šemrl 1 ; A. R. Sourour 1

1 
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Rajendra Bhatia; Peter Šemrl; A. R. Sourour. Maps on matrices that preserve the spectral radius distance. Studia Mathematica, Tome 134 (1999) no. 2, pp. 99-110. doi: 10.4064/sm-134-2-99-110

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