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.