Decompositions of non-contractive operator-valued representations of Banach algebras
We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C*- and W*-algebras; we show that interpolation space techniques can be used in place of GNS type arguments....