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

Enno KolkAnnemai 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 ) are unbounded and the topologies on the sequence spaces λ ( Φ ) and μ ( Ψ ) are given by certain F-norms. As applications we consider superposition operators on some multiplier sequence spaces of Maddox type....

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