Vol. 51, No. 1, 1974

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On the existence of support points of solid convex sets

Jürg Thomas Marti

Vol. 51 (1974), No. 1, 235–239

Let E be a separable Fréchet lattice. It is shown that a solid convex set X with void interior in E is supported at each of its boundary points if and only if the span of X is not dense in E. This result then is applied to the case of solid convex sets with void interior in real Fréchet spaces with an unconditional Schauder basis and in the real Banach lattice C(S), S compact Hausdorff.

Mathematical Subject Classification 2000
Primary: 46A40
Received: 8 November 1972
Revised: 10 August 1973
Published: 1 March 1974
Jürg Thomas Marti