2019
Том 71
№ 11

All Issues

Minimality of root vectors of operator functions analytic in an angle

Radzievskii G. V.

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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 $¦μ_k¦ > ρ$.

English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 5, pp 581-603.

Citation Example: Radzievskii G. V. Minimality of root vectors of operator functions analytic in an angle // Ukr. Mat. Zh. - 1994. - 46, № 5. - pp. 545–566.

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