Minimality of root vectors of operator functions analytic in an angle - Radzievskii, G. V. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
We study the minimality of elements x_h, j, k of canonical systems of root vectors. These systems correspond to the characteristic numbers μ_k of operator functions L(λ) analytic in an angle; we assume that operators act in a Hilbert space H. In particular, we consider the case where L(λ) = I + T(λ)C^β > 0, I is an identity operator, C is a completely continuous operator, ∥(I- λC)^−1∥ ≤ c for |λ| ≥ θ, 0 < θ < π, the operator function T(λ) is analytic, and T(λ) for |λ| < θ. It is proved that, in this case, there exists ρ > 0 such that the system of vectors C^v_x_h,j,k is minimal in H for arbitrary positive ν < 1+β, provided that ¦μ_k¦ > ρ.