广义Orlicz空间的λ—性质和一致λ—性质

λ-property and Uniformly λ-property of Generalized Orlicz Spaces Endowed with p-Amemiya Norms(1≤p≤∞)

根据各种不同理论和应用的需要,Orlicz空间有各种不同形式的推广,赋p—Amemiya范数的Orlicz空间是Orlicz空间的推广,记为LM,p空间.λ—性质和一致λ—性质是Banach空间几何理论中的重要概念,它与端点和严格凸性有着紧密的联系.本文中我们得出了LM,p空间具有λ—性质,并给出了LM,p空间具有一致λ—性质的充要条件.

According to the requirements of various theories and application, there are many generalizations of Orlicz spaces. The spaces LM,p equipped with the p-Amemi,ya norms are the generation of the Orlicz spaces. λ-property and uniformly λ-property are important geometric properties in Orliez spaces. They have close connections with extreme points and strict convexity. In this paper, we conclude that LM,p （ 1 ≤p ≤ ∞ ） spaces have the λ-property and the necessary and sufficient conditions that LM,p （1 ≤p ≤ ∞ ）spaces have the uniformly λ-property.