PRESERVERS OF MATRIX PAIRS WITH A FIXED INNER PRODUCT VALUE

Let V be the set of n×n hermitian matrices, the set of n×n symmetric matrices, the set of all effects, or the set of all projections of rank one. Let c be a real number. We characterize bijective maps φ : V → V satisfying tr (AB) = c ⇐⇒ tr (φ(A)φ(B)) = c with some additional restrictions on c , depending on the underlying set of matrices. Mathematics subject classification (2010): 15A86, 15B57.