Abstract
We study conditions on a sequence of probability measures on a commutative hypergroup K, which ensure that, for any representation π of K on a Hilbert space ℋπ and for any ξ ∈ ℋπ, converges to a π‐invariant member of ℋπ.
Highlights
The mean ergodic theorem was originally formulated by von Neumann [13] for one-parameter unitary groups in Hilbert space
K, converges in the strong topology to a projection whose range is the set of fixed points of T
Ergodic theorems in relation to the amenability concept were studied for the first time by Day
Summary
We study conditions on a sequence of probability measures {μn}n on a commutative hypergroup K, which ensure that, for any representation π of K on a Hilbert space Ᏼπ and for any ξ ∈ Ᏼπ , ( K πx (ξ)dμn(x))n converges to a π -invariant member of Ᏼπ.
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