Areshkin, G. Ya. Functional operators and families of set functions. (Russian) Zbl 0673.47002 Funkts. Anal. 26, 35-41 (1986). The author considers operators acting in functional spaces of the type F defined by N. Dunford and J. T. Schwartz in their monograph “Linear operators. General theory” (1958; Zbl 0084.104) and investigates the connection between these operators and families of set function. Especially sufficient and necessary conditions for the weak additivity, the linearity, the boundedness and the continuity of the operators considered are proved, which depend on properties of set functions. Reviewer: K.Barckow MSC: 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 46A04 Locally convex FrĂ©chet spaces and (DF)-spaces 28A10 Real- or complex-valued set functions Keywords:functional spaces of the type F; families of set function; weak additivity; linearity; boundedness; continuity Citations:Zbl 0084.104 PDFBibTeX XMLCite \textit{G. Ya. Areshkin}, Funkts. Anal. 26, 35--41 (1986; Zbl 0673.47002)