Abstract
The monomials z n form an orthogonal basis for the weighted Hardy Hilbert spaces. It is shown that versions of some natural operators defined on different weighted Hardy spaces are related (in the corresponding orthonormal bases) by a Hadamard product map. Cases in which the Hadamard multiplier is positive are established, and the results used to derive new norm and spectral information for operators on the weighted spaces from well-known information about operators on the usual (unweighted) Hardy space.
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