The A Priori Tan Theta Theorem for Eigenvectors

Abstract

Let A be a self-adjoint operator on a Hilbert space H. Assume that the spectrum of A consists of two disjoint components σ0 and σ1 such that the convex hull of the set σ0 does not intersect the set σ1. Let V be a bounded self-adjoint operator on H off-diagonal with respect to the orthogonal decomposition H = H0 ⊕ H1, where H0 and H1 are the spectral… (More)
DOI: 10.1137/06065667X

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