Normal structure and fixed point properties for some Banach algebras.

In this paper, we investigate key assumptions on some Banach algebras to have quasi-weak normal structure (resp. quasi-weak ⋆ normal structure) and to prove in particular that fixed point property for Kannan mappings is satisfied on weakly compact convex subsets in this setting. We establish some conditions on a locally compact group G for which the Fourier and Fourier–Stieltjes–Banach algebras A(G) and B(G) have quasi-normal structure. In addition, we give some examples of Banach spaces X such that L (X) (the Banach algebra of bounded linear operators on X) and some of its closed two-sided ideals associated with Fredholm perturbations have fixed point properties. Finally, we give some comments and interesting questions related to this area. [ABSTRACT FROM AUTHOR]