Relative Chebyshev Centers in L _∞ (μ,X)

Let

be a Banach space and

Y Y

a weakly

\mathcal{K} K

-analytic subspace of

X X

. In this paper we study the simultaneous proximinality in the space

L_\infty(\mu,X) L ∞ ( μ , X )

. In this sense we have proved that

L_\infty(\mu,Y) L ∞ ( μ , Y )

is simultaneously proximinal in

L_\infty(\mu,X) L ∞ ( μ , X )

if, and only if,

Y Y

is simultaneously proximinal in

X X