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Boundedness of superposition operators on some sequence spaces defined by moduli

Molder A.

Demonstratio Mathematica

2006

Vol. 39, nr 4

869-886

For a solid sequence space lambda and a sequence of modulus functions fi = (phik) let lambda(fi) = {x = (xk) : (phik(|xk|)) is an element of lambda}. Provided another solid sequence space ž and a sequence of modulus functions psi= psi(k), we give necessary and sufficient conditions for the local boundedness and boundedness of superposition operators Pf from lambda(fi)) into ž(psi) for some Banach sequence spaces lambda and ž under the assumptions that topologies on the sequence spaces lambda(fi) and ž(psi) are given by certain F-norms. As applications we characterize bounded superposition operators on some multiplier sequence spaces of Maddox type.

Some sequence spaces defined by [N,Pn] summability

Bhardwaj V., Singh N.

Demonstratio Mathematica

1999

Vol. 32, nr 3

539-546

The object of this paper is to introduce some new sequence spaces which arise from the notion of [N, pn] summability. Some topological results, certain inclusion relations and a result on matrix transformations have been discussed.