Main results: For every equicontinuous almost periodic linear representation of a group in a complete locally convex space L with the countability property, there exists the unique invariant averaging; it is continuous and is expressed by using the L-valued invariant mean of Bochner and von-Neumann. An analog of Wiener's approximation theorem for an equicontinuous almost periodic linear representation in a locally convex space with the countability property is proved.
Invariant averaging, invariant mean, almost periodic function
KHADJIEV, DJAVVAT and ÇAVUŞ, ABDULLAH
"Continuous invariant averagings,"
Turkish Journal of Mathematics: Vol. 37:
5, Article 5.
Available at: https://journals.tubitak.gov.tr/math/vol37/iss5/5