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A discrete Mellin calculus in the Toeplitz algebra
We prove that the classical Cesàro operator belongs to the Toeplitz algebra, providing an independent solution to a question raised by Barría and Halmos. Our approach is based on a discrete Mellin calculus for the sampled-ratio matrices \[ W(κ)_{jk} = \frac{1}{j+1}\, κ\!\left(\frac{k+1}{j+1}\right
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