  We study transfer operators associated to piecewise monotone interval
transformations and show that the essential spectrum is large whenever the
Banach space bounds $L^\infty$ and the transformation fails to be Markov.
Constructing a family of Banach spaces we show that the lower bound on the
essential spectral radius is optimal. Indeed, these Banach spaces realise an
essential spectral radius as close as desired to the theoretical best possible
case.
