Abstract: Let H be an infinite dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. An operator T∈B(H) is said to have the single-valued extension property(SVEP for brevity, write T∈ (SVEP)), if for every open set U∈C, the only analytic solution f:U→X of the equation (T-λI)f(λ)=0 for all λ∈U is zero function on U, where C denotes the complex number set. T∈B(H) is said to have the perturbations of the single valued extension property if T+K have the single-valued extension property for every compact operator K∈K(H). The perturbations of the single valued extension property for bounded linear operators are discussed, and the sufficient necessary condition for is given 2×2 upper triangular operator matrices for which the single valued extension property is stable under compact perturbations.

Key words: spectrum, compact perturbation, the single-valued extension property