论文标题
直径两种特性和Orlicz空间中的radon-nikodým属性
Diameter two properties and the Radon-Nikodým property in Orlicz spaces
论文作者
论文摘要
发现Banach功能晶格具有一些必要和足够的条件，使其具有ra-nikodým属性。因此，可以证明，非原子$σ$ - finite $σ$ -finite量$（ω，σ，μ）$（不一定是可分离）的orlicz空间$l_φ$，只有$φ$是$ n $ functions a radon-nikodým属性，并且只有在$ n $ function，并且满足适当的$δ_2$条件。对于Orlicz序列空间$ \ell_φ$，它具有radon-nikodým属性，并且仅当$φ$满足条件$Δ_2^0 $。在第二部分中，研究了Banach空间的单位球的均匀$ \ ell_1^2 $点之间的关系。使用这些结果，可以快速证明仅在$φ$是线性时，只有在$l_φ$等于$ l_1 $的情况下，仅当$φ$是线性时才具有Daugavet属性。另一个结果是，配备了由$ n $ functions生成的Orlicz Norm的Orlicz空间从来没有局部直径两个属性，而众所周知，当配备卢森堡标准时，它可能具有该属性。最后，结果表明，局部直径两个属性，直径两个特性，强直径的两个属性在适当条件下在$φ$的适当条件下具有卢森堡标准的功能和序列orlicens orlicz空间。
Some necessary and sufficient conditions are found for Banach function lattices to have the Radon-Nikodým property. Consequently it is shown that an Orlicz space $L_φ$ over a non-atomic $σ$-finite measure space $(Ω, Σ,μ)$, not necessarily separable, has the Radon-Nikodým property if and only if $φ$ is an $N$-function at infinity and satisfies the appropriate $Δ_2$ condition. For an Orlicz sequence space $\ell_φ$, it has the Radon-Nikodým property if and only if $φ$ satisfies condition $Δ_2^0$. In the second part the relationships between uniformly $\ell_1^2$ points of the unit sphere of a Banach space and the diameter of the slices are studied. Using these results, a quick proof is given that an Orlicz space $L_φ$ has the Daugavet property only if $φ$ is linear, so when $L_φ$ is isometric to $L_1$. The other consequence is that the Orlicz spaces equipped with the Orlicz norm generated by $N$-functions never have local diameter two property, while it is well-known that when equipped with the Luxemburg norm, it may have that property. Finally, it is shown that the local diameter two property, the diameter two property, the strong diameter two property are equivalent in function and sequence Orlicz spaces with the Luxemburg norm under appropriate conditions on $φ$.
