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Disjointly Additive Operators and Modular Spaces
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- Journal:
- Canadian Journal of Mathematics / Volume 42 / Issue 3 / 01 June 1990
- Published online by Cambridge University Press:
- 20 November 2018, pp. 508-519
- Print publication:
- 01 June 1990
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- Article
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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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