Vol. 78, No. 2, 1978

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The evolution of bounded linear functionals with application to invariant means

Hadi Kharaghani

Vol. 78 (1978), No. 2, 369–374

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 μ(f) = f dμ for f in CB(S) and μ is a measure on S which lives on a suitable set. It is shown that the evolution and convolution of m and μ coincide. The same argument carries over to prove that if X W(S), then the evolution and convolution of m and n in X are the same (a known result). The topological invariance of invariant means on X is discussed.

Mathematical Subject Classification 2000
Primary: 43A07
Secondary: 22A20
Received: 3 May 1977
Revised: 4 January 1978
Published: 1 October 1978
Hadi Kharaghani
Mathematics & Computer Science
University of Lethbridge
C568 University Hall
Alberta AB T1K 3M4