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A remark on a theorem of Caradus
Published online by Cambridge University Press: 17 April 2009
Extract
It is shown how a result of S.R. Caradus on the approximation problem can be obtained from known theorems.
Terms used here are standard (see [1] or [3]).
Let X denote a Banach space, S its unit ball in the weak topology, and X* the dual of X. In [1], the following theorem is proved: (I) If X is reflexive and X* (considered as a subspaoe of the continuous scalar-valued functions C(S) in the canonical way) is complemented in C(S), then X has the approximation property.
It is our purpose to point out that (I) is a corollary to some known theorems that yield the stronger conclusion (II) below.
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- Copyright © Australian Mathematical Society 1972