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Minimal projections in Lp-spaces

Published online by Cambridge University Press:  24 October 2008

E. J. Halton  and
W. A. Light
E. J. Halton
Affiliation:
Mathematics Department, University of Lancaster
W. A. Light
Affiliation:
Mathematics Department, University of Lancaster
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Extract

Let X be a normed linear space and let W be a proper subspace of X. A projection is a surjective linear map P: X → W such that P is idempotent. It is immediately clear that P has norm at least unity. Thus the problem of calculating the number

has some interest. The number λ(W, X) is often called the relative projectiion constant of W in X. If the infimum is attained, any attaining projection is called a minimal projection. The problems of calculating λ(W, X) for a fixed X and W or finding a minimal projection turn out to be very dificult. For example, if X = C [0, 1] with the usual supremem norm and W is the subspace of polynominals of degree at most two then λ(W, X) remains unknown as does any example of a minimal projection. One of the few places where the problem shows much tractability is the case

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 1 , January 1985 , pp. 127 - 136
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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