Turkish Journal of Mathematics
Abstract
Let Z be a Banach space and G be a closed subspace of Z. For f_1,f_2 \in Z, the distance from f_1,f_2 to G is defined by d(f_1,f_2,G) = \underset{f \in G}{\inf} max { f_1-f , f_2-f }. An element g^{\ast} \in G satisfying max { f_1-g^{\ast } , f_2-g^{\ast } } = \underset{f \in G}{\inf } max { f_1-f , f_2-f } is called a best simultaneous approximation for f_1,f_2 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).
DOI
10.3906/mat-0904-37
Keywords
Simultaneous approximation, Banach spaces
First Page
101
Last Page
112
Recommended Citation
ABU-SIRHAN, E (2012). Best simultaneous approximation in function and operator spaces. Turkish Journal of Mathematics 36 (1): 101-112. https://doi.org/10.3906/mat-0904-37
