The evolution of bounded linear functionals with application to invariant means

Hadi Kharaghani

Vol. 78 (1978), No. 2, 369–374

DOI: 10.2140/pjm.1978.78.369

Abstract

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

Milestones

Received: 3 May 1977

Revised: 4 January 1978

Published: 1 October 1978