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Petek, Tatjana
Linear algebra and its applications, 12/2015, Letnik: 487Journal Article
Given n≥2 let 2≤k≤n be fixed. We study mappings ϕ on Mn, the algebra of n×n complex matrices, that satisfy Nk(ϕ(A)ϕ(B)+ϕ(B)ϕ(A))=Nk(AB+BA) for all A, B∈Mn, where Nk(C) denotes the Ky-Fan k-norm, the sum of k greatest singular values of the matrix C. If n≥3, we additionally suppose either ϕ(μ1I)=μ2I, for some unimodular complex μ1, μ2, or, that ϕ is surjective; and when n=2, the complete description is obtained without additional assumptions.
