Band projections in spaces of regular operators
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910524598386688 |
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| author | Muñoz-Lahoz, David Tradacete, Pedro |
| author_facet | Muñoz-Lahoz, David Tradacete, Pedro |
| contents | We introduce inner band projections in the space of regular operators on a Dedekind complete Banach lattice and study some structural properties of this class. In particular, we provide a new characterization of atomic order continuous Banach lattices as those for which all band projections in the corresponding space of regular operators are inner. We also characterize the multiplication operators $L_AR_B$ which are band projections precisely as those with $A,B$ being band projections up to a scalar multiple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08318 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Band projections in spaces of regular operators Muñoz-Lahoz, David Tradacete, Pedro Functional Analysis 46B42, 46A32, 46A45, 47B65, 47B48, 47L10 We introduce inner band projections in the space of regular operators on a Dedekind complete Banach lattice and study some structural properties of this class. In particular, we provide a new characterization of atomic order continuous Banach lattices as those for which all band projections in the corresponding space of regular operators are inner. We also characterize the multiplication operators $L_AR_B$ which are band projections precisely as those with $A,B$ being band projections up to a scalar multiple. |
| title | Band projections in spaces of regular operators |
| topic | Functional Analysis 46B42, 46A32, 46A45, 47B65, 47B48, 47L10 |
| url | https://arxiv.org/abs/2310.08318 |