次Mackey空间与对偶局部完备性(英文)

Infra-Mackey spaces and dual local completeness

次Mackey空间与广义次Mackey空间被引进.对于次Mackey空间E,其强对偶(E′,β(E′,E))为局部完备等价于E为C 拟桶形也等价于E为C0 拟桶形.对于广义次Mackey空间E,强对偶(E′,β(E′,E))为局部完备等价于E为C0 拟桶形.

Infra-Mackey spaces and generalized infra-Mackey spaces are introduced.For an infra-Mackey space E,the strong dual (E′,β(E′,E)) being locally complete is equivalent to E being C-quasi-barrelled,and is also equivalent to E being C_0-quasi-barrelled.For a generalized infra-Mackey space E,the strong dual (E′,β(E′,E)) being locally complete is equivalent to E being C_0-quasi-barrelled.