Complex lindenstrauss spaces with extreme points

B. Hirsberg; A. J. Lazar

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

Complex lindenstrauss spaces with extreme points

B. Hirsberg, A. J. Lazar

School of Mathematical Sciences

Aarhus University

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

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 con* tinuous affine functions on a Choquet simplex. If X is a compact Hausdorff space and A CCtfX) is a function space then A is a Lindenstrauss space iff A is selfadjoint and Re A is a real Lindenstrauss space.

Original language	English
Pages (from-to)	141-150
Number of pages	10
Journal	Transactions of the American Mathematical Society
Volume	186
DOIs	https://doi.org/10.1090/S0002-9947-1973-0333671-7
State	Published - Dec 1973

Keywords

Choquet simplex
Lindenstrauss space
Maximal measure

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10.1090/S0002-9947-1973-0333671-7

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AB - We prove that a complex Lindenstrauss space whose unit ball has at least one extreme point is isometric to the space of complex valued con* tinuous affine functions on a Choquet simplex. If X is a compact Hausdorff space and A CCtfX) 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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KW - Lindenstrauss space

KW - Maximal measure

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Complex lindenstrauss spaces with extreme points

Abstract

Keywords

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