ON ALMOST ISOMETRIES FROM L~1 (μ) INTO L~∞(v) OR C_b (△)

Let μ,ν be measures with diem L~1(μ) =dim L~∞(ν)=∞ and ⊿ be a "subinterval" of the real line. Let E=L~∞(ν) or C_b(⊿), in this paper it turns out that the IAP for the space B(L~1(μ)→E) has a negative answer.