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- W3083359807 abstract "Given two $n times 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 $n times n$ matrix $ Asquare B := (a_{ij}b_{ij})$. Given two continuous functions $f$ and $g$ on the torus with Fourier coefficients $(f_n)$ and $(g_n)$ their convolution product $f star g$ 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 $mathcal{A} $, and a discrete group $G$ with an action $alpha _g$ of $G$ on $mathcal{A} $ by *-automorphisms, the reduced crossed product C*-algebra $mathrm {C}^*_r(mathcal{A} , alpha , G)$ 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." @default.
- W3083359807 created "2020-09-11" @default.
- W3083359807 creator A5056562596 @default.
- W3083359807 date "2020-09-03" @default.
- W3083359807 modified "2023-10-18" @default.
- W3083359807 title "The block Schur product is a Hadamard product" @default.
- W3083359807 doi "https://doi.org/10.7146/math.scand.a-121069" @default.
- W3083359807 hasPublicationYear "2020" @default.
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