Complex Lindenstrauss spaces with extreme points

Hirsberg, B.; Lazar, A. J.

doi:10.1090/S0002-9947-1973-0333671-7

Complex Lindenstrauss spaces with extreme points
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by B. Hirsberg and A. J. Lazar

Trans. Amer. Math. Soc. 186 (1973), 141-150

DOI: https://doi.org/10.1090/S0002-9947-1973-0333671-7

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Abstract:

We prove that a complex Lindenstrauss space whose unit ball has at least one extreme point is isometric to the space of complex valued continuous affine functions on a Choquet simplex. If X is a compact Hausdorff space and $A \subset {C_{\text {C}}}(X)$ is a function space then A is a Lindenstrauss space iff A is selfadjoint and Re A is a real Lindenstrauss space.

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