Nonstandard Representation Theory of Standard Operators Defined on the Space of Bochner Integrable Functions

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.