Bounds on perturbations of self-adjoint operators
Suppose the spectrum of the selfadjoint operator \(T^0\) is known while the spectrum of the perturbed selfadjoint operator \(T=T^0+V\) is unknown. If \(V\) is a bounded operator, the spectrum of \(T\) is expected to be shifted from that of \(T^0\) by no more than the norm \(|V|\) of \(V\). It is pointed out by \textit{M. M. Skriganov} [Proc. Steklov Inst. Math. 171 (1987; Zbl 0615.47004)] that in certain situations the size of this shift is much less than \(|V|\). The paper under review improves it to give some tighter bounds on this shift. The result is also compared with those to be obtained by using Temple's inequality and the generalized Temple's inequality and some applications are given.
scientific article; zbMATH DE number 930182