Using a double sequence of modulus functions and a solid double scalar sequence space, we determine F-seminorm and F-norm topologies for certain generalized linear spaces of double sequences. The main results are applied to the topologization of double sequence spaces related to 4-dimensional matrix methods of summability.
For a solid sequence space λ and a sequence of modulus functions Φ=(φk), let λ(Φ) = {x=(xk) : Φ(x)=(φk(|xk|))∈λ} . Provided another sequence of moduli Ψ = (ψk), we give necessary and sufficient conditions for the local boundedness and boundedness of superposition operators from (w0)p(Φ) into lq(Ψ) in the case 1≤p,q<∞.
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