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Complex Lindenstrauss spaces with extreme points


Authors: B. Hirsberg and A. J. Lazar
Journal: Trans. Amer. Math. Soc. 186 (1973), 141-150
MSC: Primary 46B05; Secondary 46E15
DOI: https://doi.org/10.1090/S0002-9947-1973-0333671-7
MathSciNet review: 0333671
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0333671-7
Keywords: Lindenstrauss space, maximal measure, Choquet simplex
Article copyright: © Copyright 1973 American Mathematical Society

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