On the sum of best simultaneously proximinal subspaces

Authors : Mahmoud RAWASHDEH, Sh ALSHARİF, Wb DOMİ

Pages : 595-602

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Publication Date : 2014-08-01

Article Type : Research Paper

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 dinsert ignore into journalissuearticles values(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