论文标题
关于Banach束和Banach模块的反射性特性
On the reflexivity properties of Banach bundles and Banach modules
论文作者
论文摘要
在本文中，我们研究了在$σ$ - 精细的测量空间上可分开可分开的Banach束的反射性型特性。我们的两个主要结果是： - 束的纤维均匀凸（具有凸的通用模量），并且仅当其$ l^p $ septions的空间均匀地凸出（1，\ infty）$中的每个$ p \。 - 捆绑纤维的纤维是反身的，并且仅当其$ l^p $ sections的空间反射时。 这些结果推广了Lebesgue-Bochner空间的众所周知的相应相应。
In this paper we investigate some reflexivity-type properties of separable measurable Banach bundles over a $σ$-finite measure space. Our two main results are the following: - The fibers of a bundle are uniformly convex (with a common modulus of convexity) if and only if the space of its $L^p$-sections is uniformly convex for every $p\in(1,\infty)$. - The fibers of a bundle are reflexive if and only if the space of its $L^p$-sections is reflexive. These results generalise the well-known corresponding ones for Lebesgue-Bochner spaces.
