Real structure in complex 𝐿₁-preduals

Wulbert, Daniel E.

doi:10.1090/S0002-9947-1978-0472918-8

Real structure in complex $L_{1}$-preduals
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by Daniel E. Wulbert

Trans. Amer. Math. Soc. 235 (1978), 165-181

DOI: https://doi.org/10.1090/S0002-9947-1978-0472918-8

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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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and subspaces of

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