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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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Boundedly complete $M$-bases and complemented subspaces in Banach spaces
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by William J. Davis and Ivan Singer PDF
Trans. Amer. Math. Soc. 175 (1973), 187-194 Request permission

Abstract:

Subsequences of boundedly complete M-bases need not be boundedly complete. An example of a somewhat reflexive space is given whose dual and one of whose factors fail to be somewhat reflexive. A geometric description of boundedly complete M-bases is given which is equivalent to the definitions of V. D. Milman and W. B. Johnson. Finally, certain M-bases for separable spaces give rise to proper complemented subspaces.
References
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 175 (1973), 187-194
  • MSC: Primary 46B15
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0317011-5
  • MathSciNet review: 0317011