Injective Banach Lattices.
Semigroups S for which the Banach algebra is injective are investigated and an application to the work of O. Yu. Aristov is described.
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.
In this paper, following the -adic integration theory worked out by A. F. Monna and T. A. Springer [4, 5] and generalized by A. C. M. van Rooij and W. H. Schikhof [6, 7] for the spaces which are not -compacts, we study the class of integrable -adic functions with respect to Bernoulli measures of rank . Among these measures, we characterize those which are invertible and we give their inverse in the form of series.