The block Schur product is a Hadamard product - Christensen, Erik (MATHEMATICA SCANDINAVICA, 2020)
Given two n × n matrices A = (a_ij) and B=(b_ij) with entries in B(H) for some Hilbert space H, their block Schur product is the n × n matrix AB := (a_ijb_ij). Given two continuous functions f and g on the torus with Fourier coefficients (f_n) and (g_n) their convolution product f g has Fourier coefficients (f_n g_n). 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 α _g 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.