A Note on Unconditional Bases
Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 369-372
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A sequence (xi) in a Banach space X is a Schauder basis for X provided for each x∊X there is a unique sequence of scalars (a i) such that 1.1 convergence in the norm topology. It is well known [1] that if (xi) is a (Schauder) basis for X and (fi) is defined by 1.2 where then fi(xj) = δij and fi∊X* for each positive integer i.A sequence (xi) is a éasic sequence in X if (xi) is a basis for [xi], where the bracketed expression denotes the closed linear span of (xi).
Holub, J. R.; Retherford, J. R. A Note on Unconditional Bases. Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 369-372. doi: 10.4153/CMB-1972-067-1
@article{10_4153_CMB_1972_067_1,
author = {Holub, J. R. and Retherford, J. R.},
title = {A {Note} on {Unconditional} {Bases}},
journal = {Canadian mathematical bulletin},
pages = {369--372},
year = {1972},
volume = {15},
number = {3},
doi = {10.4153/CMB-1972-067-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-067-1/}
}
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