论文标题
Banach功能空间的拓扑双重
Topological duals of Banach function spaces
论文作者
论文摘要
本文研究了BANACH功能空间（BFS）的拓扑双重双重。我们假设一个有限的度量，但我们的参数扩展到一般的局部凸函数空间，其拓扑是由满足常规BFS公理的eminorm产生的。双重识别是随机变量的另一个直接总和（köthdual）的直接总和，一个纯有限加性测量的空间和$ l^\ infty $的an灭者。在重新安排不变空间的特殊情况下，双重的第二部分消失，我们获得了各种经典和新的双重性结果，例如在Lebesgue，Orlicz，Lorentz-Orlicz的空间和有限时刻的空间。除了重排的不变空间之外，我们还发现了Musielak-Orlicz空间的拓扑双重偶数以及与一般凸风险度量相关的空间。
This paper studies topological duals of Banach function spaces (BFS). We assume a finite measure but our arguments extend to general locally convex function spaces whose topology is generated by seminorms that satisfy the usual BFS axioms. The dual is identified with the direct sum of another space of random variables (Köthe dual), a space of purely finitely additive measures and the annihilator of $L^\infty$. In the special case of rearrangement invariant spaces, the second component in the dual vanishes and we obtain various classical as well as new duality results e.g. on Lebesgue, Orlicz, Lorentz-Orlicz spaces and spaces of finite moments. Beyond rearrangement invariant spaces, we find the topological duals of Musielak-Orlicz spaces and those associated with general convex risk measures.
