论文标题
Banach空间上的有限拓扑及其在经济理论中的某些用途：评论
Bounded topologies on Banach spaces and some of their uses in economic theory: a review
论文作者
论文摘要
审查了有关实际Banach空间上拓扑t的有界和凸有界变体BT和CBT的已知结果。重点是t = w（p*，p）和t = m（p*，p）的病例，该病例是弱*，而双重Banach空间p*上的Mackey拓扑。已知凸的有限的Mackey拓扑CBM（P*，P）与M相同（P*，P）。至于BM（P*，P），它的猜想比M（P*，P）强，或者等效地不是矢量拓扑（除非P是反射性的）。有限的Mackey和经济理论中有限的弱拓扑的某些用途及其应用。还审查的是在一般的Banach空间Y及其凸变体（CBW和CKW）上，有界弱和紧凑的弱拓扑，BW（Y，Y*）和KW（Y，Y*）。
Known results are reviewed about the bounded and convex bounded variants, bT and cbT, of a topology T on a real Banach space. The focus is on the cases of T = w(P*, P) and of T = m(P*, P), which are the weak* and the Mackey topologies on a dual Banach space P*. The convex bounded Mackey topology, cbm(P*, P), is known to be identical to m(P*, P). As for bm(P*, P), it is conjectured to be strictly stronger than m(P*, P) or, equivalently, not to be a vector topology (except when P is reflexive). Some uses of the bounded Mackey and the bounded weak* topologies in economic theory and its applications are pointed to. Also reviewed are the bounded weak and the compact weak topologies, bw(Y, Y*) and kw(Y, Y*), on a general Banach space Y, as well as their convex variants (cbw and ckw).
