Talk:James's theorem

Formulation of the theorem[edit]

I am not sure to understand the formulation of this theorem. Should'nt it rather be stated as: "a Banach space B is reflexive if and only if every continuous linear functional on B restricted to the closed unit ball attains its maximum"? — Preceding unsigned comment added by Polucs (talk • contribs)

Same thing. Yours is perhaps more accurate. The way it is now seems more common, though. Jmath666 (talk) 07:18, 5 August 2011 (UTC)[reply]

The references[edit]

Hi, I worked on James's theorem in my 1965 PhD thesis and I've just seen that this isn't noted in the article. I simplified James's proof and extended it to a general locally convex space. This appeared in John D. Pryce. Weak compactness in locally convex spaces. Proc. Amer. Math. Soc., 17(1):148–155, 1966.

I did more in this area, though maybe less relevant to this article: John D. Pryce. A device of R. J. Whitley’s applied to pointwise compactness in spaces of continuous functions. Proceedings of the London Mathematical Society, s3- 23(3):532–546, 1971. John Pryce2 (talk) 05:03, 12 September 2022 (UTC)[reply]