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INNER AMENABILITY OF LAU ALGEBRAS

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*R. Nasr-Isfahani*

**Address.** Department of Mathematics, University of Isfahan, 81744
Isfahan, IRAN
**E-mail:** isfahani@sci.ui.ac.ir

**Abstract.** A concept of amenability for an arbitrary Lau algebra
called inner amenability is introduced and studied. The inner amenability
of a discrete semigroup

is characterized by the inner amenability of its convolution semigroup
algebra. Also, inner amenable Lau algebras are characterized by several
equivalent
statements which are similar analogues of properties characterizing left
amenable Lau algebras.

**AMSclassification.** 43A07, 46H05

**Keywords.** Lau algebra, inner amenable, topological inner invariant
mean.