Abstract
Many of the classical theorems in approximation theory can be formulated in terms of convergence of a sequence of linear operators to the identity operator. To illustrate this, we consider one example in detail, obtaining Bernstein's proof of the Weierstrass approximation theorem. For each n ≥ 1, define the operator B n from C[0,1] into the polynomials of degree at most n by setting, for f ∈ C[0,1].
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© 2001 Springer-Verlag Berlin Heidelberg
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(2001). The Choquet boundary and approximation theory. In: Phelps, R.R. (eds) Lectures on Choquet’s Theorem. Lecture Notes in Mathematics, vol 1757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48719-0_9
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DOI: https://doi.org/10.1007/3-540-48719-0_9
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41834-4
Online ISBN: 978-3-540-48719-7
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