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Tame Köthe Sequence Spaces are Quasi-Normable

Krzysztof Piszczek (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

We show that every tame Fréchet space admits a continuous norm and that every tame Köthe sequence space is quasi-normable.

The continuity of superposition operators on some sequence spaces defined by moduli

Enno Kolk, Annemai Raidjõe (2007)

Czechoslovak Mathematical Journal

Let λ and μ be solid sequence spaces. For a sequence of modulus functions Φ = ( ϕ k ) let λ ( Φ ) = { x = ( x k ) ( ϕ k ( | x k | ) ) λ } . Given another sequence of modulus functions Ψ = ( ψ k ) , we characterize the continuity of the superposition operators P f from λ ( Φ ) into μ ( Ψ ) for some Banach sequence spaces λ and μ under the assumptions that the moduli ϕ k ( k ...

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