Proximity maps for certain spaces
Bull. Korean Math. Soc. 1997 Vol. 34, No. 2, 259-271
Mun Bae Lee and Song Ho Park
Sogang University, Sogang University
Abstract : Let $X$ be a Banach space, $G$ a closed subspace of $X$ and $(S,\Omega,\mu)$ be a $\sigma$-finite measure space. The object of this paper is to discuss the proximity map of $L_p(S,G)$ in $L_p(S,X)$ where $p$ is a positive number. Results on proximity maps in $C(S,X)$ and $L(X,Y)$ are presented.
Keywords : best approximation, continuous (linear, Lipschitz continuous) proximity map, 1-complemented, uniformly convex
MSC numbers : 41A65, 46B20
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