数学物理学报(英文版) ›› 1994, Vol. 14 ›› Issue (4): 475-478.
• 论文 • 上一篇
定光桂, 黄森忠
Ding Guanggui, Huang Senzhong
摘要: Let (Ω, ∑,μ) be a measure space and (Xω)ω∈Ω a family of closed linear subspaces of some Banach space X. Let L1 (μ, (Xω)) be the linear subspace of the Bochner space L1 (μ,X) given by L1 (μ, (Xω)):={f ∈ L1 (μ,X):f(ω) ∈ Xω for all ω ∈ Ω}. Suppose that each Xω is of type p with constant 1 for some fixed p > 1. Two results are obtained:(1) If E ⊆ L1 (μ, (Xω)) is isomorphic to some L1 space with constant less than 21-1/p, then there is a projection from L1 (μ,X) onto E. (2) If E ⊆ L1 (μ, (Xω)) is a L1,λ space with λ small enough then E is complemented in L1 (μ, (Xω)). These results generalize early results of Dor[3], Alspach and Johnson[1].