Some natural families of M-ideals. (English) Zbl 0687.46010

We characterize the subspaces of \(L^ 1\) and the translation-invariant subspaces of \({\mathcal M}(G)\) which are duals of M-ideals, and we describe their M-ideal predual. We show that there is a separable dual which is L- complemented in its bidual but is not the dual of an M-ideal. We show that a separable \({\mathcal L}^{\infty}\)-space which is isomorphic to an M- ideal is actually isomorphic to \(c_ 0(N)\).
Reviewer: D.Li


46B20 Geometry and structure of normed linear spaces
46B25 Classical Banach spaces in the general theory
43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
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