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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
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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- V. Montesinos, Solution to a problem of S. Rolewicz, Studia Math. 81 (1985), 65--69. MR 87c:46024
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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:
http://dx.doi.org/10.1090/S0002-9939-96-03122-X
PII:
S 0002-9939(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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