Lipschitz spectrum preserving mappings on algebras of matrices Original Research Article

It is proved that for any Lipschitz mapping T on the algebra Mn of n × n matrices over the complex numbers satisfying T(0) = 0 and σ(T(A) − T(B)) subset of σ(A − B), A, B set membership, variant Mn, there exists an invertible matrix U set membership, variant Mn such the T(A) = UAU−1 for all A set membership, variant Mn or T(A) = UAtU−1 for all A set membership, variant Mn.