Variational Principles for Eigenvalues of Compact Nonselfadjoint Operators

Let T be a linear compact operator on a Hilbert space H, Aj be its eigenvalues, IA,1 > /& > ,..., rj be the moduli of the real parts of the eigenvalues ordered so that r, > r2 .... Note that rj is not necessarily equal to 1 Re ;ljj. Let Lj be the eigensubspace of T corresponding to Aj, yj be the eigensubspace of T corresponding to rj, zj = Cjk,, i L,, aj = xi=, -k Mk. Let tj be the moduli of the imaginary parts of the eigenvalues, t, > t, > ,..., flj = C’,=, i N,, Nj be the eigensubspace of T corresponding to tj, Ly -I zj = H, the sign i denotes the direct sum, LI denotes the direct complement in H.