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• W3100776505 abstract "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(σ0, σ1), the spectrum of the perturbed operator L = A+V consists of two isolated parts ω0 and ω1, which appear as perturbations of the respective spectral sets s0 and s1. Furthermore, we have the sharp upper bound ||EA(σ0) - EL(ω0)|| ≤ sin (arctan(||V||/d)) on the difference of the spectral projections EA(σ0)) and EL(ω0)) corresponding to the spectral sets σ0 and ω0 of the operators A and L. We give a new proof of this bound in the case where ||V|| < d." @default.
• W3100776505 created "2020-11-23" @default.
• W3100776505 creator A5021072645 @default.
• W3100776505 date "2016-01-01" @default.
• W3100776505 modified "2023-10-18" @default.
• W3100776505 title "Alternative proof of the a priori tan Θ theorem" @default.
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• W3100776505 doi "https://doi.org/10.1134/s0040577916010074" @default.
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