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RETRACTED ARTICLE: Some applications of BP-theorem in approximation theory

Abstract

In this paper we apply Bishop-Phelps property to show that if X is a Banach space and GX is the maximal subspace so that G = {x* ∈ X*|x*(y)=0; ÅyG} is an L-summand in X*, then L 1(Ω,G) is contained in a maximal proximinal subspace of L 1(Ω,X).

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References

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Author information

Correspondence to I. Sadeqi.

Additional information

This article has been retracted at the request of the EiC due to redundant publication; it was previously published with the title “Application of Bishop-Phelps theorem in the approximation theory” in journal J. Nonlinear Sci. Appl., 3, no. 2 (2010), pp. 144-147.

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Sadeqi, I., Zarghami, R. RETRACTED ARTICLE: Some applications of BP-theorem in approximation theory. Anal. Theory Appl. 27, 220–223 (2011). https://doi.org/10.1007/s10496-011-0220-6

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Key words

  • Bishop-Phelps theorem
  • support point
  • proximinality
  • L-projection

AMS (2010) subject classification

  • 46E99