- Turkish Journal of Mathematics
- Vol: 36 Issue: 1
- Best simultaneous approximation in function and operator spaces
Best simultaneous approximation in function and operator spaces
Authors : Eyad Abu-sirhan
Pages : 101-112
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Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :Let Z be a Banach space and G be a closed subspace of Z. For f1,f2 \in Z, the distance from f1,f2 to G is defined by d(f1,f2,G) = \underset{f \in G}{\inf} max {||f1-f||, ||f2-f||}. An element g\ast \in G satisfying max {||f1-g\ast ||, || f2-g\ast ||} = \underset{f \in G}{\inf } max {|| f1-f||, ||f2-f||} is called a best simultaneous approximation for f1,f2 from G. In this paper, we study the problem of best simultananeous approximation in the space of all continuous X-valued functions on a compact Hausdorff space S; C(S,X), and the space of all Bounded linear operators from a Banach space X into a Banach space Y; L(X,Y).Keywords : Simultaneous approximation, Banach spaces