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dc.contributor.author | Ding, Chun![]() |
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dc.contributor.author | De Jeu, Marcel![]() |
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dc.date.accessioned | 2024-10-02T05:15:00Z | |
dc.date.available | 2024-10-02T05:15:00Z | |
dc.date.issued | 2023-07 | |
dc.description | DATA AVAILABILITY : Data sharing is not applicable to this paper as no datasets were generated or analysed during the current research. | en_US |
dc.description.abstract | After collecting a number of results on interval and almost interval preserving linear maps and vector lattice homomorphisms, we show that direct systems in various categories of normed vector lattices and Banach lattices have direct limits, and that these coincide with direct limits of the systems in naturally associated other categories. For those categories where the general constructions do not work to establish the existence of general direct limits, we describe the basic structure of those direct limits that do exist. A direct system in the category of Banach lattices and contractive almost interval preserving vector lattice homomorphisms has a direct limit. When the Banach lattices in the system all have order continuous norms, then so does the Banach lattice in a direct limit. This is used to show that a Banach function space over a locally compact Hausdorff space has an order continuous norm when the topologies on all compact subsets are metrisable and (the images of) the continuous compactly supported functions are dense. | en_US |
dc.description.department | Mathematics and Applied Mathematics | en_US |
dc.description.librarian | am2024 | en_US |
dc.description.sdg | None | en_US |
dc.description.sponsorship | China Scholarship Council. | en_US |
dc.description.uri | http://link.springer.com/journal/11117 | en_US |
dc.identifier.citation | Ding, C. & De Jeu, M. 2023, 'Direct limits in categories of normed vector lattices and Banach lattices', Positivity, vol. 27, no. 39, pp. 1-32. https://DOI.org/10.1007/s11117-023-00992-8. | en_US |
dc.identifier.issn | 1385-1292 (print) | |
dc.identifier.other | 1572-9281 (online) | |
dc.identifier.other | 10.1007/s11117-023-00992-8 | |
dc.identifier.uri | http://hdl.handle.net/2263/98420 | |
dc.language.iso | en | en_US |
dc.publisher | Springer | en_US |
dc.rights | © The Author(s) 2023. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License. | en_US |
dc.subject | Vector lattice | en_US |
dc.subject | Normed vector lattice | en_US |
dc.subject | Banach lattice | en_US |
dc.subject | Direct limit | en_US |
dc.subject | Inductive limit | en_US |
dc.subject | (Almost)interval preserving map | en_US |
dc.subject | Order continuous norm | en_US |
dc.title | Direct limits in categories of normed vector lattices and Banach lattices | en_US |
dc.type | Article | en_US |