Multiplicatively local spectrum preserving maps on Matrices

Let Mn(C) be the algebra of all n n complex matrices, and x a nonzero vector x۰ ۲ Cn.We show that if two maps φ۱ and φ۲ from Mn(C) into itself satis es φ۱(T)φ۲(S) (x۰) = TS (x۰) (T; S ۲ Mn(C));if and only if there exist two unitary matrices A;B ۲ Mn(C) such that φ۱(T) = ATB for allT ۲ Mn(C) and φ۲(T) = B TA for all T =۲Mn;x۰ .

کلیدواژه ها:

Nonlinear preserver ، local spectrum ، matrix