On Characteristics of the Range of Integral Operators
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911910830538752 |
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| author | Gerlach, Moritz Glück, Jochen |
| author_facet | Gerlach, Moritz Glück, Jochen |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_14397 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Characteristics of the Range of Integral Operators Gerlach, Moritz Glück, Jochen Functional Analysis Primary 47B34, Secondary: 47B65 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. |
| title | On Characteristics of the Range of Integral Operators |
| topic | Functional Analysis Primary 47B34, Secondary: 47B65 |
| url | https://arxiv.org/abs/2205.14397 |