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Functional operators and families of set functions. (Russian) Zbl 0673.47002

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 Fréchet spaces and (DF)-spaces
28A10 Real- or complex-valued set functions

Citations:

Zbl 0084.104
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