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Continuity of superposition operators on \(w_ 0\) and \(W_ 0\). (English) Zbl 0741.47007
Summary: The complete characterization is given for continuity of the superposition operator acting from the space of all sequences or all functions Cesáro strongly summable to zero into the space \(\ell_ 1\) or \(L_ 1([0,\infty))\), respectively. Properties as well as criteria for uniform continuity of such kind of operator are essentially different from analogical ones for superposition operator acting from \(\ell_ 1\) to \(\ell_ 1\) or from \(L_ 1([1,\infty))\) to \(L_ 1([1,\infty))\).

MSC:
47B38 Linear operators on function spaces (general)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
46B45 Banach sequence spaces
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