On some locally convex FK spaces

2022/05/30 by Leonetti, Paolo, Orhan, Cihan
#FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN)

paper · doi:10.48550/arxiv.2205.15048

Abstract

We provide necessary and/or sufficient conditions on vector spaces V of real sequences to be a Fréchet space such that each coordinate map is continuous, that is, to be a locally convex FK space. In particular, we show that if c₀₀(I)⊆ V⊆ ℓ_∞(I) for some ideal I on ω, then V is a locally convex FK space if and only if there exists an infinite set S⊆ ω for which every infinite subset does not belong to I.

Related

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