An Open Problem about Complemented Subspace

In paper [2], L.E. Dor asked the followirg question: Given 11 so that if T: l_p→L_p is an isomorphic embedding with, then Tl_p is complemented in L_p? In this paper, using the result of [3], we show that the above question has a positive answer.     

Lp空间中的投影算子

在文[1]中,L.E.Dor 讨论了 L_1空间中的投影算子,他证明了下面的结果。定理 设μ和 v 均为测度,T∶L:(v)→L_(?)(μ)为一同构嵌入且满足‖T‖·‖T~(-1)‖≤λ(2~(1/2))。则存在从 L_1(μ)到 T 的值域上的投影算子 P,使得