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Banach spaces that admit support sets |
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| Authors: | J M Borwein J D Vanderwerff |
| Institution: | Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 J. D. Vanderwerff ; Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 |
| 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. |
| Keywords: | Proper support point support set uncountable biorthogonal system convex set |
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