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- فارسی
Common fixed point properties and amenability of a class of Banach algebras
Common fixed point properties and amenability of a class of Banach algebras
- Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111 , Isfahan, Iran
- School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran.
- Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111 , Isfahan, Iran.
Abstract
Let A be a Lau algebra and let SA be the semigroup of all positive functionals in A with norm one. We obtain some equivalent conditions for left amenability of A in terms of a common fixed point property and the Hahn–Banach property. We then apply these results for certain Lau algebras on a locally compact group G to give characterizations for amenability of G.
Keywords: Lau algebra; Common fixed point property; Left amenability; Fourier algebra; Group algebra; Topological semigroup.