Bhatia, Rajendra ; Šemrl, Peter ; Sourour, A. (1999) Maps on matrices that preserve the spectral radius distance Studia Mathematica, 134 (2). pp. 99-110. ISSN 0039-3223
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Official URL: http://journals.impan.gov.pl/sm/
Abstract
Let ø be a surjective map on the space of n x n complex matrices such that r(ø(A)-ø(B))=r(A-B) for all A,B, where r(X) is the spectral radius of X. We show that must ø 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, ø is real linear up to a translation.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Institute of Mathematics of the Polish Academy of Sciences. |
| ID Code: | 97466 |
| Deposited On: | 11 Feb 2013 04:47 |
| Last Modified: | 11 Feb 2013 04:47 |
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