Entire functions and compact operators with $S_p$-imaginary component
  We study operators of the form X+Y where Y has a finite p-th Schatten norm (p<2), and X is self-adjoint and of Hilbert-Schmidt class. Our study is based on new theorems on zero distribution of entire functions of finite order. 
Vladimir Matsaev (1) and Mikhail Sodin (1) ((1) Tel Aviv University)