Biduals of Banach spaces with bases
Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 101-103
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R. C. James [2] (or see p. 7ff of [3]) gave a useful representation of the bidual of any space with a shrinking basis. This note gives a representation of the bidual of any space with a basis.Our notation follows that of [3], where undefined terms can be found. Let {en} be a basic sequence with coefficient functionals {fn}. We will assume {en} is bimonotone; that is. The space {en}LIM is the set of scalar sequences {an} so that ∥{an}∥ = . We will abuse notation and squate such {an} with the formal sum Σ anen.
Bellenot, Steven F. Biduals of Banach spaces with bases. Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 101-103. doi: 10.1017/S0017089500005826
@article{10_1017_S0017089500005826,
author = {Bellenot, Steven F.},
title = {Biduals of {Banach} spaces with bases},
journal = {Glasgow mathematical journal},
pages = {101--103},
year = {1985},
volume = {26},
number = {1},
doi = {10.1017/S0017089500005826},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500005826/}
}
[1] 1.Bellenot, S. F., The J-sum of Banach spaces, J. Functional Analysis 48 (1982), 95–106. Google Scholar | DOI
[2] 2.James, R. C., Bases and reflexivity of Banach spaces, Ann. of Math. 52 (1950), 518–527. Google Scholar | DOI
[3] 3.Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces I Sequence Spaces (Springer Verlag, 1977). Google Scholar
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