On the sum of best simultaneously proximinal subspaces

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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