Relative injectivity and amenable actions

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.