Operator convex functions of several variables

  title={Operator convex functions of several variables},
  author={Frank Hansen},
The functional calculus for functions of several variables associates to each tuple x = (xl, •••,.x fc) of selfadjomt operators on Hilbert spaces Hl9~-,Hk an operator/(.x) in the tensor product ^//j)® ••• ®B(Hk). We introduce the notion of generalized Hessian matrices associated with /. Those matrices are used as the building blocks of a structure theorem for the second Frechei differential of the map x-*f(x). As an application we derive that functions with positive semi-definite generalized… CONTINUE READING

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