Numerical range with respect to a family of projections
  In this note we introduce the concept of the numerical range of a bounded linear operator with respect to a family of projections. We give a precise definition and elaborate on its connection to the classical numerical range as well as to generalisations such as the quadratic numerical range and block numerical range. 
W.Dada, N. Erkur\c{s}un and J. Kerner
math.SP