An interlacing theorem for eigenvalues of self-adjoint operators (Q1089882)

The following result is proved: if A, B are self-adjoint operators, \(B=A+\lambda P\) where \(\lambda\in {\mathbb{R}}\) and P is a rank one orthogonal projection then the eigenvalues of A and B interlace in any interval where the total spectral multiplicity is finite. Reviewer's note: Under slightly more general conditions (A, B unbounded, and the spectrum of one of them has no accumulation points in the interval considered) the result is proved in {\S} 3.7 of: \textit{M. G. Krejn} [Mat. Sb., n. Ser. 33(75), 597-626 (1953; Zbl 0052.123)].