Minimality of root vectors of operator functions analytic in an angle
Abstract
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 $|\arg λ| ≥ θ,\; 0 < θ < π$, the operator function $T(λ)$ is analytic, and $T(λ)$ for $|\arg λ| < θ$. 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 $¦μ_k¦ > ρ$.
Published
25.05.1994
How to Cite
Radzievskii, G. V. “Minimality of Root Vectors of Operator Functions Analytic in an Angle”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 46, no. 5, May 1994, pp. 545–566, https://umj.imath.kiev.ua/index.php/umj/article/view/5718.
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Section
Research articles