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The L1-version of the Diliberto–Straus algorithm in C(T × S)

Published online by Cambridge University Press:  20 January 2009

W. A. Light  and
S. M. Holland
W. A. Light
Affiliation:
Mathematics Department, Texas A. ' M. University, College Station, Texas
S. M. Holland
Affiliation:
Mathematics Department, Texas A. ' M. University, College Station, Texas
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Let (S, Σ, μ) and (T, Θ, v) be two measure spaces of finite measure where we assume S, T are compact Hausdorff spaces and μ, v are regular Borel measures. We construct the product measure space (T x S, >, Φ σ) in the usual way. Let G = [gl, g2, …, gp] and H = [hl, h1, …, hm be finite dimensional subspaces of C(S) and C(T) respectivelywhere G and H are also Chebyshev with respect to the L1-norm. Note that a subspace Y of a normed linear space X is Chebyshev if each x ∈X possesses exactly one best approximation y ∈Y. For example, in C(S) with the L1-norm, the subspace of polynomials of degree at most n is a Chebyshev subspace. This is an old theorem of Jackson. Now set

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 1 , February 1984 , pp. 31 - 45
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

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