Vol. 35, No. 3, 1970

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On the Choquet boundary for a nonclosed subspace of C(S)

Tae Geun Cho

Vol. 35 (1970), No. 3, 575–580

In this paper, it is proved that if a separating (not necessarily closed) subspace X of C(S) which contains all the constant functions is generated by a weakly compact convex subset, then the peak points for X are dense in the Choquet boundary for X. In order to prove the theorem the extremal structure of convex subsets of the conjugate space of a normed linear space is studied.

Mathematical Subject Classification
Primary: 46.55
Received: 7 November 1969
Published: 1 December 1970
Tae Geun Cho