On the boundary of the numerical range of some Jacobi operators
  In this paper, we study the numerical range of Jacobi operators and it is shown that under certain conditions, the boundary of the numerical range of these operators can be non-round only at the points where it touches the essential spectrum. It is further shown that these points cannot be the eigenvalue of the Jacobi operators. 
R. Birbonshi, A. Patra and P. D. Srivastava
math.SP