Normal matrix compressions
  The recently developed theory of higher--rank numerical ranges originated in problems of error correction in quantum information theory but its mathematical implications now include a quite satisfactory understanding of \emph{scalar} compressions of complex matrices. Here our aim is to make some first steps in the more general program of understanding \emph{normal} compressions. We establish some general principles for the program and make a detailed study of rank--two normal compressions. 
John Holbrook, Nishan Mudalige, Rajesh Pereira
math.FA