Nonstandard representation theory of standard operators defined on the space of Bochner integrable functions
(2002) Mathematical Logic Quarterly — Vol. 48, n° 3, p. 379-390 (2002)
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- Abstract
- We introduce and study several nonstandard representations of Banach-valued operators defined on the space of Bochner integrable functions. They will be less restrictive than the usual standard representation. In particular, without any hypothesis, we shall find a representation whose kernel belongs to a space of "extended Bochner integrable functions", introduced by Zimmer by using Loeb measures.
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Vanderputten, L. (2002). Nonstandard representation theory of standard operators defined on the space of Bochner integrable functions. Mathematical Logic Quarterly, 48(3), 379-390. https://doi.org/10.1002/1521-3870(200204)48:3<379::AID-MALQ379>3.0.CO;2-5 (Original work published 2002)