Disjointly Additive Operators and Modular Spaces

Labuda, Iwo

Canadian journal of mathematics, Tome 42 (1990) no. 3, pp. 508-519

Résumé

By now the literature concerning the representation of disjointly additive functionals and operators is quite extensive. A few entries on the subject are [6, 7, 8, 11, 20, 21]. In [7, 8, 17] further references can be found, in [7] the “prehistory” of the subject is also discussed.To quote a typical result, we may take a 1967 theorem of Drewnowski and Orlicz ([6] Th. 3.2, [17] 12.4) which asserts that, under proper assumptions, an abstract modular (= disjointly countably additive functional) p on a “substantial“ subspace D of L ° can be realized by the formula .

Détail

DOI : 10.4153/CJM-1990-026-5

Mots-clés : 47H99, 46A99, 46E30, Disjointly additive nonlinear operator, modular space, Abramovich extension

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