A Property in Vector-Valued Function Spaces

This paper deals with a property which is equivalent to generalised-lushness for separable spaces. It thus may be seemed as a geometrical property of a Banach space which ensures the space to have the Mazur-Ulam property. We prove that a Banach space X enjoys this property if and only if C(K, X) enjoys this property. We also show the same result holds for L-infinity(mu, X) and L-1(mu, X).