Saturation theorems for families of dual operators (Q796012)

This paper deals with the saturation behaviour of a family of dual operators \(\{\) T'\({}_ t\}\), where \(\{T_ t\}\) is a commutative, strong approximation process on a Banach space X, satisfying a so-called Voronovskaya-type relation. It turns out that the saturation order of \(\{\) T'\({}_ t\}\) is the same as that for \(\{T_ t\}\), and the saturation class of \(\{\) T'\({}_ t\}\) can be characterized in a natural way. Applications are given for semigroups of operators, recovering some results of \textit{K. de Leeuw} [Math. Z. 73, 219-234 (1960; Zbl 0094.105)], and for convolution integrals.