We recall (1) elements of the theory of spectral operators, due to Dunford (2) elements of the theory of decomposable operators, due to Foias and Apostol and (3) in the setting of tracial von Neumann algebras, elements of the theory of Haagerup-Schultz projections and related results. We show a relation between spectrality of operators and angles between Haagerup-Schultz projections. This leads to a proof that Voiculescu's circular operator is not spectral. This is joint work with Amudhan Krishnaswamy-Usha.