Conditions for massiveness of the range of the derivation of a Banach algebra and associated differential operators (Q1099372)

From the authors introduction. The main result in this paper claims that images of all differential operators in a Banach algebra are enough massive unless the differentiation is locally algebraic. As consequences, several generalizations of a theorem of \textit{C. Le Page} [C. R. Acad. Sci., Paris, Sér. A 265, 235-237 (1967; Zbl 0158.141)], a characterization of elements which are nilpotent or algebraic modulo radical, some conditions of subadditivity and continuity of the spectral radius etc. have been obtained.