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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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