A Supplement to James ’ Theorem ∗ Hwa - Long Gau and Ngai - Ching Wong
نویسنده
چکیده
The famous R. James’ Theorem (see [3–7] and [8]) asserts that a Banach space E is reflexive if and only if the closed unit ball UE has the James’ property, i.e. every continuous linear functional f of E attains its supremum in UE. James’ Theorem does not hold, however, for general normed spaces [6]. We prove in this talk that a normed space X is reflexive if and only if UX has the separation property. Since the separation property is equivalent to, in Banach spaces, and implies, in general, James’ property, our results can be viewed as a supplement to James’.
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