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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Extending continuous linear functionals in convergence vector spaces
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by S. K. Kranzler and T. S. McDermott PDF
Trans. Amer. Math. Soc. 200 (1974), 149-168 Request permission

Abstract:

Let $(E,\tau )$ be a convergence vector space, $M$ a subspace of $E$, and $\varphi$ a linear functional on $M$ continuous in the induced convergence structure. Sufficient and sometimes necessary conditions are given that (1) $\varphi$ has a continuous linear extension to the $\tau$-adherence $\bar M$ of$M$; (2) $\varphi$ has a continuous linear extension to $E$; (3) $\bar M$ is $\tau$-closed; (4) every $\tau$-closed convex subset of $E$ is $\sigma (E,E’)$-closed. Several examples are included illustrating the extent and limitations of the theory presented.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 200 (1974), 149-168
  • MSC: Primary 46A15
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0407557-4
  • MathSciNet review: 0407557