Completeness of unbounded convergences
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- by M. A. Taylor
- Proc. Amer. Math. Soc. 146 (2018), 3413-3423
- DOI: https://doi.org/10.1090/proc/14007
- Published electronically: March 30, 2018
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Abstract:
As a generalization of almost everywhere convergence to vector lattices, unbounded order convergence has garnered much attention. The concept of boundedly $uo$-complete Banach lattices was introduced by N. Gao and F. Xanthos, and has been studied in recent papers by D. Leung, V. G. Troitsky, and the aforementioned authors. We will prove that a Banach lattice is boundedly $uo$-complete iff it is monotonically complete. Afterwards, we study completeness-type properties of minimal topologies; minimal topologies are exactly the Hausdorff locally solid topologies in which $uo$-convergence implies topological convergence.References
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Bibliographic Information
- M. A. Taylor
- Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6Gย 2G1, Canada
- Email: mataylor@ualberta.ca
- Received by editor(s): August 28, 2017
- Received by editor(s) in revised form: October 31, 2017
- Published electronically: March 30, 2018
- Additional Notes: The author acknowledges support from NSERC and the University of Alberta.
- Communicated by: Thomas Schlumprecht
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3413-3423
- MSC (2010): Primary 46A40, 46A16, 46B42
- DOI: https://doi.org/10.1090/proc/14007
- MathSciNet review: 3803666