<i>FK</i> Spaces in Which the Sequence of Coordinate Vectors is Bounded 论文

摘要

The work presented in this paper was initially motivated by the following question of A. Wilansky: “Is there a smallest FK-space E in which is bounded?” Here FK-space means a complete linear metric space of real or complex sequences x = ( x i ) upon which the coordinate functional x → x t are continuous for each i (see [ 10 , p. 202]), and An FK-space need not be locally convex, and therein lies the difficulty of the problem since it is easy to see that l 1 is the smallest locally convex FK -space.