On a Subspace Perturbation Problem

Konstantin Makarov University of Missouri-Columbia

Let A and V be bounded self-adjoint operators on a separable Hilbert space. Assume that the spectrum of A consists of two disjoint parts Δ and Σ such that dist(Δ, Σ) > 0. Denote by {P (s)} the real analytic family of spectral projections of A+sV uniquely determined by the requirement that P (0) is the spectral projection of A associated with the set Δ. Under various assumptions on the perturbation V and mutual disposition of the sets Δ and Σ we obtain (optimal) sufficient conditions on the magnitude of the coupling constant s ∈ ℝ that ensure the strict inequality ∥P (s) − P (0)∥ < 1.

This is a joint work with V. Kostrykin and A. K. Motovilov.