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Invariant Means on Dense Subsemigroups of Topological Groups

Published online by Cambridge University Press:  20 November 2018

Anthony To-Ming Lau
Anthony To-Ming Lau*
Affiliation:
University of Alberta, Edmonton, Alberta
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Let S be a topological semigroup (i.e., S is a semigroup with a Hausdorff topology such that the mapping from S × S to S defined by (s, t) → s ⋅ t for all s, t in S is continuous when S × S has the product topology) and C(S) be the space of bounded continuous real valued functions on S. For each ƒ in C(S) and a in S, define || ƒ || = sup {|ƒ(s)|: s ∈ S} (sup norm of ƒ); raƒ(s) = ƒ(sa) and laƒ(s) = ƒ(as) for all s in S.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 5 , October 1971 , pp. 797 - 801
Copyright
Copyright © Canadian Mathematical Society 1971

Footnotes

This work was supported by NRC Grant A-7679.

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