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We show that every tame Fréchet space admits a continuous norm and that every tame Köthe sequence space is quasi-normable.
In this note we study the Bade property in the C(K,X) and c(X) spaces. We also characterize the spaces X = C(K,R) such that c(X) has the uniform λ-property.
Let and be solid sequence spaces. For a sequence of modulus functions let . Given another sequence of modulus functions , we characterize the continuity of the superposition operators from into for some Banach sequence spaces and under the assumptions that the moduli
It is proved that a Fréchet space is quasinormable if, and only if, every quotient space satisfies the density condition of Heinrich. This answers positively a conjecture of Bonet and Díaz
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