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Bibliographic Details
Main Authors: Gerlach, Moritz, Glück, Jochen
Format: Preprint
Published: 2022
Subjects:
Online Access:https://arxiv.org/abs/2205.14397
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Table of Contents:
  • We show that a positive operator between $L^p$-spaces is given by integration against a kernel function if and only if the image of each positive function has a lower semi-continuous representative with respect to a suitable topology. This is a consequence of a new characterization of kernel operators on general Banach lattices as those operators whose range can be represented over a fixed countable set of positive vectors. Similar results are shown to hold for operators that merely dominate a non-trivial kernel operator.