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Transactions of the American Mathematical Society

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

 

 

Boundedly complete $ M$-bases and complemented subspaces in Banach spaces


Authors: William J. Davis and Ivan Singer
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
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0317011-5
Keywords: Basis, Markushevich basis, reflexivity, projection, complemented subspace, somewhat reflexive
Article copyright: © Copyright 1973 American Mathematical Society