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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Real structure in complex $ L\sb{1}$-preduals


Author: Daniel E. Wulbert
Journal: Trans. Amer. Math. Soc. 235 (1978), 165-181
MSC: Primary 46B25
DOI: https://doi.org/10.1090/S0002-9947-1978-0472918-8
MathSciNet review: 472918
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Abstract: Call a complex Banach space selfadjoint if it is isometrically isomorphic to a selfadjoint subspace of a $ C(X,{\mathbf{C}})$-space. B. Hirsberg and A. Lazar proved that if the unit ball of a complex Lindenstrauss space, E, has an extreme point, then E is selfadjoint. Here we will give a characterization of selfadjoint Lindenstrauss spaces, and construct a nonselfadjoint complex Lindenstrauss space.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0472918-8
Keywords: Lindenstrauss space, Hirsberg-Lazar theorem
Article copyright: © Copyright 1978 American Mathematical Society