Facial characterizations of complex lindenstrauss spaces

Ellis, A. J. ; Rao, T. S. S. R. K. ; Roy, A. K. ; Uttersrud, U. (1981) Facial characterizations of complex lindenstrauss spaces Transactions of the American Mathematical Society, 286 (1). pp. 173-186. ISSN 0002-9947

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Official URL: http://www.ams.org/journals/tran/1981-268-01/S0002...

Related URL: http://dx.doi.org/10.1090/S0002-9947-1981-0628453-7


We characterize complex Banach spaces A whose Banach dual spaces are L1(μ) spaces in terms of L-ideals generated by certain extremal subsets of the closed unit ball K of A. 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-compact sets of extreme points of K, whereas the nonseparable spaces necessitate usage of the w-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 Cc(X) which are complex Lindenstrauss spaces.

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