Abstract
Let X be a Banach holomorphic function space on the unit disk. A linear polynomial approximation scheme for X is a sequence of bounded linear operators \(T_n:X\rightarrow X\) with the property that, for each \(f\in X\), the functions \(T_n(f)\) are polynomials converging to f in the norm of the space. We completely characterize those spaces X that admit a linear polynomial approximation scheme. In particular, we show that it is not sufficient merely that polynomials be dense in X.
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First author supported by a Grant from NSERC. Second author supported by Grants from NSERC and the Canada Research Chairs program.
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Mashreghi, J., Ransford, T. Linear polynomial approximation schemes in Banach holomorphic function spaces. Anal.Math.Phys. 9, 899–905 (2019). https://doi.org/10.1007/s13324-019-00312-y
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DOI: https://doi.org/10.1007/s13324-019-00312-y