Continuity of superposition operators on \(w_ 0\) and \(W_ 0\). (English) Zbl 0741.47007

Płuciennik, Ryszard

Commentat. Math. Univ. Carol. 31, No. 3, 529-542 (1990).

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

Keywords:

Lebesgue sequence space; Lebesgue function space; continuity of the superposition operator; space of all sequences or all functions Cesáro strongly summable