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Let A be a self-adjoint operator in a separable Hilbert space. We assume that the spectrum of A consists of two isolated components σ0 and σ1 and the set σ1 is in a finite gap of the set σ1. It is known that if V is a bounded additive self-adjoint perturbation of A that is off-diagonal with respect to the partition spec(A) = σ0 ∪ σ1, then for $$\left\| V \right\| < \sqrt 2 d$$ , where d = dist(σ...
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