Geodesic
The Convergence of Series for Various Choices of Sign in Banach Spaces
Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 475-480

Voir la notice de l'article provenant de la source Cambridge University Press

1. Let (xn, Xn) denote a basis for a Banach space (X, ∥ • ∥) of measurable functions in (0, 1).It is shown in [2] and [9] that the equivalence of the norms and ∥ • ∥ is equivalent to the unconditionality of the basis (xn, Xn). In [8] a weaker relationship between these norms is exploited to establish the existence of an element of L1(E) for each E ⊂ (0, 1), |£| > 0, whose Haar series expansion is conditionally convergent in the norm of L\(E).In this note, a Lemma of Orlicz [7] is generalized to provide a relationship between , and the changes in sign that are tolerated in without disruption of norm convergence. 
Shirey, James. The Convergence of Series for Various Choices of Sign in Banach Spaces. Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 475-480. doi: 10.4153/CJM-1975-056-2
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