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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Banach spaces that admit support sets
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by J. M. Borwein and J. D. Vanderwerff PDF
Proc. Amer. Math. Soc. 124 (1996), 751-755 Request permission

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
  • 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 1996 American Mathematical Society
  • 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