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 ⊆ ∞(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
On some locally convex FK spaces
Paolo Leonetti
Primo
;
2023-01-01
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 ⊆ ∞(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
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