Groenewald, G.J.Ter Horst, S.Ran, A.C.M.Jaftha, J.2019-05-272019-05-272019Groenewald, G.J. et al. 2019. A Toeplitz-like operator with rational symbol having poles on the unit circle. II. The spectrum. (In Bolotnikov, V., Ter Horst, S., Ran, A.C.M. & Vinnikov, V., eds. Interpolation and realization theory with applications to control theory: 133-154). [https://doi.org/10.1007/978-3-030-11614-9_7]978-3-030-11613-2978-3-030-11614-9 (Online)0255-01562296-4878 (Online)http://hdl.handle.net/10394/32439https://link.springer.com/chapter/10.1007/978-3-030-11614-9_7https://doi.org/10.1007/978-3-030-11614-9_7This paper is a continuation of our study of a class of Toeplitz-like operators with a rational symbol which has a pole on the unit circle. A description of the spectrum and its various parts, i.e., point, residual and continuous spectrum, is given, as well as a description of the essential spectrum. In this case, the essential spectrum need not be connected in C . Various examples illustrate the results.enUnbounded Toeplitz operatorSpectrumEssential spectrumBook chapter