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Fixed point characterization of left amenable Lau algebras. (English) Zbl 1065.43004
Summary: The present paper deals with the concept of left amenability for a wide range of Banach algebras known as Lau algebras. It gives a fixed point property characterizing left amenable Lau algebras $$\mathcal{A}$$ in terms of left Banach $$\mathcal{A}$$-modules. It also offers an application of this result to some Lau algebras related to a locally compact group $$G$$, such as the Eymard-Fourier algebra $$A(G)$$, the Fourier-Stieltjes algebra $$B(G)$$, the group algebra $$L^1(G)$$, and the measure algebra $$M(G)$$. In particular, it presents some equivalent statements which characterize the amenability of locally compact groups.

##### MSC:
 43A07 Means on groups, semigroups, etc.; amenable groups 43A10 Measure algebras on groups, semigroups, etc. 43A20 $$L^1$$-algebras on groups, semigroups, etc. 46H05 General theory of topological algebras
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