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Relative injectivity and amenable actions

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1758)

Abstract

In this chapter, we introduce and study a notion of relative injectivity for Banach G-modules, a topic which has already an unmistakable cohomological flavour.

As before, modules of L∞ functions attached to regular G-spaces have an important place in the discussion. It will turn out that these modules link relative injectivity to a dynamical concept introduced by R. Zimmer : amenability of group actions.

As long as we consider merely relative injectivity, there will be no assumption on the topological group G. Then, for L∞ spaces and amenable actions, we shall have to assume local compactness and second countability.

Keywords

  • Banach Space
  • Topological Group
  • Short Exact Sequence
  • Topological Vector Space
  • Extension Problem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2001 Springer-Verlag Berlin Heidelberg

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(2001). Relative injectivity and amenable actions. In: Monod, N. (eds) Continuous Bounded Cohomology of Locally Compact Groups. Lecture Notes in Mathematics, vol 1758. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44962-0_3

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  • DOI: https://doi.org/10.1007/3-540-44962-0_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42054-5

  • Online ISBN: 978-3-540-44962-1

  • eBook Packages: Springer Book Archive