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Invariant means and fixed point properties on completely regular spaces

Published online by Cambridge University Press:  17 April 2009

Marvin W. Grossman
Marvin W. Grossman
Affiliation:
Department of Mathematics, Temple University, Philadelphia, Pennsyivania, USA.
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Abstract

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Two theorems are presented which characterize the existence of multiplicative left invariant means on a given algebra of unbounded continuous functions on a topological semigroup S in terms of certain common fixed point properties of actions of S on completely regular spaces. Also a lattice formulation of a related result of Theodore Mitchell for the case of bounded functions is shown to be equivalent to a certain common fixed point property on Bauer simplexes.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 2 , April 1977 , pp. 203 - 212
Copyright
Copyright © Australian Mathematical Society 1977

References

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