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Amenability of representations and invariant Hahn–Banach theorems

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Abstract

Invariant Hahn–Banach theorems are proved in the context of right amenable, weakly almost periodic representations of semigroups on locally convex spaces. Applications are made to invariant means, invariant measures, and to Banach limits on weakly almost periodic flows. Additionally, invariant linear Hahn–Banach extension operators are shown to exist on suitable invariant subspaces of Banach spaces. The key construct on which these results depend is the lifting of a representation on a semigroup S to its coefficient compactification, the minimal compactification of S for which the lift is injective.

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Notes

  1. To avoid cumbersome notation, we use the same notation for the two representations. Context will make clear which representation is being referenced.

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  1. Department of Mathematics, George Washington University, Washington, DC, 20052, USA

    H. D. Junghenn

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  1. H. D. Junghenn
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Correspondence to H. D. Junghenn.

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Junghenn, H.D. Amenability of representations and invariant Hahn–Banach theorems. J Anal 28, 931–949 (2020). https://doi.org/10.1007/s41478-020-00223-3

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  • DOI: https://doi.org/10.1007/s41478-020-00223-3

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