A Fréchet sequence space (cf. Fréchet space) such that all the coordinates $P_n$ defined by $P_n(x)=x_n$ are continuous linear functionals (cf. Linear functional). (Some authors include local convexity in the definition.)
An FK space that is also a Banach space is called a BK-space.
BK-space. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=BK-space&oldid=41996