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The evolution of bounded linear functionals with application to invariant means

The evolution of bounded linear functionals with application to invariant means

Let S be a topological semigroup and let X be a left translation invariant, left introverted closed subspace of CB(S).Let m and μ be elements of X*, where β(f) -\fdμ for / in CB(S) and μ is a measure on S which lives on a suitable set.It is shown that …