Geodesic
FK Spaces in Which the Sequence of Coordinate Vectors is Bounded
Canadian journal of mathematics, Tome 25 (1973) no. 5, pp. 973-978

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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 → xt 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 l1 is the smallest locally convex FK-space. 
Ruckle, William H. FK Spaces in Which the Sequence of Coordinate Vectors is Bounded. Canadian journal of mathematics, Tome 25 (1973) no. 5, pp. 973-978. doi: 10.4153/CJM-1973-102-9
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