  We extend the results of our previous paper "C*-algebras and numerical linear
algebra" to cover the case of "unilateral" sections. This situation bears a
close resemblance to the case of Toeplitz operators on Hardy spaces, in spite
of the fact that the operators here are far from Toeplitz operators. In
particular, there is a short exact sequence 0 --> K --> A --> B --> 0 whose
properties are essential to the problem of computing the spectra of self
adjoint operators.
