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Disjointly Additive Operators and Modular Spaces
Published online by Cambridge University Press: 20 November 2018
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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 .
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- Copyright © Canadian Mathematical Society 1990