Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T22:43:37.646Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
(3)Light, W. A. and Cheney, E. W.Some best-approximation theorems in tensor-product spaces. Math. Proc. Cambridge Philos. Soc. 89 (1981), 385390.CrossRefGoogle Scholar
(4)Singer, I.Best approximation in normed linear spaces by elements of linear subspaces (Springer-Verlag, 1970).CrossRefGoogle Scholar