INVARIANT AVERAGINGS AND THEIR APPLICATIONS
Khadjiev, Ayupov · Uzbek Mathematical Journal · 2024
A definition of an invariant averaging for a linear representation of a group on a locally convex space is given. We obtain a description of all locally compact groups H such that every strongly continuous linear representation of H on a quasi-complete locally convex space has an invariant averaging. A connection between an invariant averaging and an L-valued invariant mean of von-Neumann and Bochner is established. A counter-example is given to von-Neumann and Bochner’s theorem on the spectrum of an almost periodic function. A description of all prime almost periodic actions of an commutative group on a Banach algebra is obtained.