Weak compactness and metrizability of Mackey*-bounded sets in Fréchet spaces (2018). Akadémiai Kiadó, 1-15.

[:es]Juan Carlos Ferrando (University Miguel Hernandez of Elche) and Jerzy Kąkol (University Adam Mickiewicz of Poznań).
Abstract. Motivated by the density condition in the sense of Heinrich for Fréchet spaces and by some results of Schlüchtermann and Wheeler for Banach spaces, we characterize in terms of certain weakly compact resolutions those Fréchet spaces enjoying the property that each bounded subset of its Mackey* dual is metrizable. We also characterize those Köthe echelon Fréchet spaces λp(A) as well as those Fréchet spaces C_k (X) of real-valued continuous functions equipped with the compact-open topology that enjoy this property.
Keywords. Bounded resolution; weakly compact resolution; G-base of neighborhoods; K-analytic space; SWKA space; SWCG space[:]