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In this paper, by virtue of coderivatives, we investigate sensitivity analysis of parametric vector set-valued optimization problems in Banach spaces. Several examples are provided to illustrate the main results.

Abstract. Let H : M m → M m be a holomorphic function of the algebra M m of complex m × m matrices. Suppose that H is orthogonally additive and orthogonally multiplicative on self-adjoint elements. We show that either the range of H consists of zero trace elements, or there is a scalar sequence {λ n } and an invertible S in M m such thatHere, x t is the transpose of the matrix x. In the latter case, we always have the first representation form when H also preserves zero products. We also discuss the cases where the domain and the range carry different dimensions.