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Linear operators in the space of regulated functions. (English) Zbl 0790.47023
A real-valued function \(f:[a,b] \to \mathbb{R}\) is said to be regulated if it has two-sided limits at all points. Let \(G(a,b)\) be the space of all regulated functions and let \(G_ L(a,b)\) be the space of all regulated functions on \([a,b]\) which are left continuous. \(G(a,b)\) [respectively, \(G_ L(a,b)]\) is a Banach space under the supnorm. The author gives integral representations for the bounded and compact linear operations from \(G_ L(a,b)\) into \(G(a,b)\).

MSC:
47B38 Linear operators on function spaces (general)
47B07 Linear operators defined by compactness properties
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
28A25 Integration with respect to measures and other set functions
26A39 Denjoy and Perron integrals, other special integrals
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