Best simultaneous approximation in function and operator spaces

Authors : Eyad ABU-SIRHAN

Pages : 101-112

View : 12 | Download : 6

Publication Date : 0000-00-00

Article Type : Research Paper

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 dinsert ignore into journalissuearticles values(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; Cinsert ignore into journalissuearticles values(S,X);, and the space of all Bounded linear operators from a Banach space X into a Banach space Y; Linsert ignore into journalissuearticles values(X,Y);.
Keywords : Simultaneous approximation, Banach spaces