Resumen de The block Schur product is a Hadamard product
Given two n×n matrices A=(aij) and B=(bij) with entries in B(H) for some Hilbert space H, their block Schur product is the n×n matrix A□B:=(aijbij). Given two continuous functions f and g on the torus with Fourier coefficients (fn) and (gn) their convolution product f⋆g has Fourier coefficients (fngn). Based on this, the Schur product on scalar matrices is also known as the Hadamard product.
We show that for a C*-algebra A, and a discrete group G with an action αg of G on A by *-automorphisms, the reduced crossed product C*-algebra C∗r(A,α,G) possesses a natural generalization of the convolution product, which we suggest should be named the Hadamard product.
We show that this product has a natural Stinespring representation and we lift some known results on block Schur products to this setting, but we also show that the block Schur product is a special case of the Hadamard product in a crossed product algebra.
