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
2023
Locally convex FK space Ideal convergence Tall idea
Leonetti, Paolo; Orhan, Cihan
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2145992
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