一些局部凸空间的算子刻划

CHARACTERIZATIONS OF THE OPERATORS FOR SOME LOCALLY CONVEX SPACES

用线性算子刻划了Mackey空间,囿空间,Banach-Mackey空间和Mazur空间等局部凸空间.设X,Y都是非零的Hausdroff局部凸空间,则有定理1 X是Mackey空间的充要条件为:对L_s(X,Y)的每个均衡凸紧子集M,如果M′将Y′的均衡凸σ(Y′,Y)闭的等度连续集映成X′的凸集,那么就有M等度连续.定理3 X是囿空间的充要条件为:每个从X到Y的一致有界的线性算子族都是等度连续的.定理5 X是Banach-Mackey空间当且仅当L_s(X,Y)中的每个点点有界集都是一致有界的.定理8 X是Mazur空间当且仅当每个从X到Y的序列连续的线性算子都是弱连续的.

In this paper, some locally convex spaces, such as Mackey spaces, bornologic spaces, Banach-Mackey spaces and Mazur spaces, are characterized with the linear operators on them. Let X and Y be nonzero Hausdroff locally convex spaces, then we haveTheorem 1 X is a Mackey space if and only if every balanced convex compact subset M of L,(X, Y), such that M' maps the balanced convex a(Y',Y) closed equicontinuous subset of Y' onto convex subset of X', is equicontinuous.Theorem 3 X is a bornologic space if and only if every uniformly bounded set of linear operators from X to Y is equicontinuous.Theorem 5 X is a Banach-Mackey space if and only if every pointwise bounded subset of L(X, Y) is uniformly bounded.Theorem 8 X is a Mazur space if and only if every squentially continuous linear operator from X to Y is weakly continuous.