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Best approximation in LP (I, X)

Published online by Cambridge University Press:  24 October 2008

Roshdi Khalil
Roshdi Khalil
Affiliation:
Department of Mathematics, Kuwait University, Kuwait
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Extract

Let T be a measure space and m a finite measure on T. The space of p-Bochner integrable functions defined on T with values in a Banach space X is denoted by Lp(T, X). It is well known (1) that Lp (T, X) is a Banach space under the norm

A subspace E in a Banachh space F is said to be proximinal if for each xF there is at least one xE such that

The element y is called best approximant of x in E.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 2 , September 1983 , pp. 277 - 279
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

(1)Diestel, J. and Uhl, J. R.Vector measures. Math. Surveys 15, 1977.Google Scholar
(2)Kthe, G.Topological vector spaces (Springer-Verlag, 1969).Google Scholar
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(4)Singer, I.Best approximation in normed linear spaces by elements of linear subspaces (Springer-Verlag, 1970).CrossRefGoogle Scholar