A semishrinking basis which is not shrinking

Retherford, J. R.

doi:10.1090/S0002-9939-1968-0225144-0

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)

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A semishrinking basis which is not shrinking
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by J. R. Retherford

Proc. Amer. Math. Soc. 19 (1968), 766

DOI: https://doi.org/10.1090/S0002-9939-1968-0225144-0

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References

William J. Davis and David W. Dean, The direct sum of Banach spaces with respect to a basis, Studia Math. 28 (1966/67), 209–219. MR 213850, DOI 10.4064/sm-28-2-209-219
A. Pełczyński and W. Szlenk, An example of a non-shrinking basis, Rev. Roumaine Math. Pures Appl. 10 (1965), 961–966. MR 203432
J. R. Retherford, Shrinking bases in Banach spaces, Amer. Math. Monthly 73 (1966), 841–846. MR 201954, DOI 10.2307/2314177
Albert Wilansky, The basis in Banach space, Duke Math. J. 18 (1951), 795–798. MR 44026