Kostrykin, V.V.KostrykinMakarov, K.A.K.A.MakarovMotovilov, A.K.A.K.Motovilov2022-03-032022-03-032003https://publica.fraunhofer.de/handle/publica/20338110.1090/S0002-9939-03-06917-X2-s2.0-0142231084We discuss the problem of perturbation of spectral subspaces for linear self-adjoint operators on a separable Hilbert space. Let A and V be bounded self-adjoint operators. Assume that the spectrum of A consists of two disjoint parts sigma and Sigma such that d = dist(sigma, Sigma) > 0. We show that the norm of the difference of the spectral projections E-A(sigma) and E-A+V({lambda\dist(lambda, sigma) < d/2}) for A and A + V is less than one whenever either (i) &PAR;V&PAR; < 2/2+pi d or (ii) parallel toVparallel to < 1/2 d and certain assumptions on the mutual disposition of the sets &sigma; and &USigma; are satisfied.en621510journal article