Facial characterizations of complex Lindenstrauss spaces
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- by A. J. Ellis, T. S. S. R. K. Rao, A. K. Roy and U. Uttersrud PDF
- Trans. Amer. Math. Soc. 268 (1981), 173-186 Request permission
Abstract:
We characterize complex Banach spaces $A$ whose Banach dual spaces are ${L^1}(\mu )$ spaces in terms of $L$-ideals generated by certain extremal subsets of the closed unit ball $K$ of ${A^{\ast }}$. Our treatment covers the case of spaces $A$ containing constant functions and also spaces not containing constants. Separable spaces are characterized in terms of ${w^{\ast }}$-compact sets of extreme points of $K$, whereas the nonseparable spaces necessitate usage of the ${w^{\ast }}$-closed faces of $K$. Our results represent natural extensions of known characterizations of Choquet simplexes. We obtain also a characterization of complex Lindenstrauss spaces in terms of boundary annihilating measures, and this leads to a characterization of the closed subalgebras of ${C_{\mathbf {C}}}(X)$ which are complex Lindenstrauss spaces.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 268 (1981), 173-186
- MSC: Primary 46B10; Secondary 46A55
- DOI: https://doi.org/10.1090/S0002-9947-1981-0628453-7
- MathSciNet review: 628453