## 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

### MSC:

 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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