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Banach spaces that admit support sets


Authors: J. M. Borwein and J. D. Vanderwerff
Journal: Proc. Amer. Math. Soc. 124 (1996), 751-755
MSC (1991): Primary 46B03, 46B20
DOI: https://doi.org/10.1090/S0002-9939-96-03122-X
MathSciNet review: 1301010
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Abstract: It is shown that the existence of a closed convex set all of whose points are properly supported in a Banach space is equivalent to the existence of a certain type of uncountable ordered one-sided biorthogonal system. Under the continuum hypothesis, we deduce that this notion is weaker than the existence of an uncountable biorthogonal system.


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Additional Information

J. M. Borwein
Affiliation: Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6

J. D. Vanderwerff
Affiliation: Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
Address at time of publication: Department of Mathematics, Walla Walla College, College Place, Washington 99324

DOI: https://doi.org/10.1090/S0002-9939-96-03122-X
Keywords: Proper support point, support set, uncountable biorthogonal system, convex set
Received by editor(s): May 24, 1994
Additional Notes: The first author’s research was supported in part by an NSERC research grant and by the Shrum endowment.
The second author is a NSERC postdoctoral fellow.
Communicated by: Dale Alspach
Article copyright: © Copyright 1996 American Mathematical Society

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