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Banach spaces that admit support sets
Author(s):
J.
M.
Borwein;
J.
D.
Vanderwerff
Journal:
Proc. Amer. Math. Soc.
124
(1996),
751-755.
MSC (1991):
Primary 46B03, 46B20
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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.
References:
- [E]
- R. Engleking, Outline of General Topology, North-Holland, Amsterdam, 1989.
- [FG]
- M. Fabian and G. Godefroy, The dual of every Asplund space admits a projectional resolution of identity, Studia Math. 91 (1988), 141--151. MR 90b:46032
- [FiG]
- C. Finet and G. Godefroy,, Biorthogonal systems and big quotient spaces, Contemp. Math., vol. 85, Amer. Math. Soc., Providence, RI, 1989, pp. 87--110. MR 90f:46022
- [K]
- D. Kutzarova, Convex sets containing only support points in Banach spaces with an uncountable minimal system, C. R. l'Acad. Bulg. Science 39 (1986), 13--14. MR 88f:46041
- [L]
- A. J. Lazar, Points of support for closed convex sets, Illinois J. Math. 25 (1981), 302--305. MR 82h:46029
- [M]
- V. Montesinos, Solution to a problem of S. Rolewicz, Studia Math. 81 (1985), 65--69. MR 87c:46024
- [N]
- S. Negrepontis, Banach spaces and topology. MR 86i:46018
- [S]
- C. Stegall, The Radon-Nikodým property in conjugate Banach spaces, Trans. Amer. Math. Soc. 206 (1975), 213--223. MR 51:10581
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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:
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
Copyright of article:
Copyright
1996,
American Mathematical Society
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