On the sum of best simultaneously proximinal subspaces

Year 2014, Volume: 43 Issue: 4, 595 - 602, 01.08.2014

Mahmoud Rawashdeh , Sh. Al-sharif W.b. Domi

Abstract

Let X be a Banach space and G a subspace of X. A point g0 ∈ G
is said to be a best simultaneous approximation for a bounded set
A ⊆ X if d(A, G) = inf
g∈G
sup
a∈A
ka − gk = sup
a∈A
ka − g0k. In this paper we
prove that if F and G are two subspaces of a Banach space X such
that G is reflexive and F is simultaneously proximinal, then F + G is
simultaneously proximinal provided that F ∩ G is finite dimensional
and F + G is closed. Some other related results are also presented.

Keywords

Approximation, simultaneously

References

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