Published online by Cambridge University Press: 20 November 2018
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 (ai) 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).