Best simultaneous approximation in metric spaces

Abstract EN

For a Banach space X and an increasing subadditive continuous function 99 on [0, 00) with f(0) = 0, iet us denote by L (1,X), the space 01 aii A-valued tp-integrable functions / : I -* I on a certain positive complete a-finite measure space (/, ^2, fj,) with ip / (t)|| d / j,(t) < 00 and / (X) = {xj.) : Yl ip\\ xk \ \ < 00, xj.

G X 1 fc=i The aim of this paper is to prove that for a closed separable subspace G of X, L (/, G) is simultaneously proximmal in L (1, X) li and only li G is simultaneously proximmal in X.

Other result on simultaneous approximation oi / (G) in / (X) is presented.

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