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A Schoenberg-type correspondence for semigroups of linear maps on the matrix algebras M_n

We will recall the definition and basic properties of k-positive and k-superpositive maps, and then use Schürmann's Schoenberg correspondence to characterize the generators of semigroups of such maps acting on M_n. Based on joint work with B.V.R. Bhat and Purbayan Chakraborty.