Infinite Riesz decompositions
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- by A. W. Wickstead
- Proc. Amer. Math. Soc. 147 (2019), 4581-4584
- DOI: https://doi.org/10.1090/proc/14560
- Published electronically: June 27, 2019
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Abstract:
This paper commences the study of infinite analogues of the Riesz decomposition property for ordered vector spaces and ordered normed spaces. A complete result is obtained in the normed case and partial results in general.References
- Charalambos D. Aliprantis and Rabee Tourky, Cones and duality, Graduate Studies in Mathematics, vol. 84, American Mathematical Society, Providence, RI, 2007. MR 2317344, DOI 10.1090/gsm/084
- Leonard Gillman and Melvin Henriksen, Rings of continuous functions in which every finitely generated ideal is principal, Trans. Amer. Math. Soc. 82 (1956), 366–391. MR 78980, DOI 10.1090/S0002-9947-1956-0078980-4
- W. A. J. Luxemburg and A. C. Zaanen, Riesz spaces. Vol. I, North-Holland Mathematical Library, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1971. MR 0511676
- G. L. Seever, Measures on $F$-spaces, Trans. Amer. Math. Soc. 133 (1968), 267–280. MR 226386, DOI 10.1090/S0002-9947-1968-0226386-5
- A. W. Wickstead, Spaces of operators with the Riesz separation property, Indag. Math. (N.S.) 6 (1995), no. 2, 235–245. MR 1338329, DOI 10.1016/0019-3577(95)91246-R
- A. C. Zaanen, Riesz spaces. II, North-Holland Mathematical Library, vol. 30, North-Holland Publishing Co., Amsterdam, 1983. MR 704021, DOI 10.1016/S0924-6509(08)70234-4
Bibliographic Information
- A. W. Wickstead
- Affiliation: Mathematical Sciences Research Centre, Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland, United Kingdom
- MR Author ID: 182585
- Email: a.wickstead@qub.ac.uk
- Received by editor(s): January 9, 2018
- Received by editor(s) in revised form: January 29, 2019
- Published electronically: June 27, 2019
- Communicated by: Thomas Schlumprecht
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 4581-4584
- MSC (2010): Primary 06F20, 46B40
- DOI: https://doi.org/10.1090/proc/14560
- MathSciNet review: 4011495