  We generalize the solution theory for a class of delay type differential
equations developed in a previous paper, dealing with the Hilbert space case,
to a Banach space setting. The key idea is to consider differentiation as an
operator with the whole real line as the underlying domain as a means to
incorporate pre-history data. We focus our attention on the issue of causality
of the differential equations as a characterizing feature of evolutionary
problems and discuss various examples. The arguments mainly rely on a variant
of the contraction mapping theorem and a few well-known facts from functional
analysis.
