Vol. 79, No. 1, 1978

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Almost periodic functions on semidirect products of transformation semigroups

Hugo Junghenn

Vol. 79 (1978), No. 1, 117–128

The notion of semidirect product of two transformation semigroups is introduced, and its space of almost periodic functions is expressed as a tensor product. The general techniques developed are applied to the special case of a semidirect product S○τT of two semigroups. As a consequence new results are obtained on the characterization of the almost periodic compactification of S○τT as a semidirect product of compact semigroups. A related result is the splitting of the enveloping semigroup of a semidirect product of certain flows into a semidirect product of enveloping semigroups.

Mathematical Subject Classification 2000
Primary: 54H15
Secondary: 22A20, 43A60
Received: 22 July 1977
Published: 1 November 1978
Hugo Junghenn