Functiones et Approximatio Commentarii Mathematici

An estimate for the number of eigenvalues of a Hilbert--Schmidt operator in a half-plane

Michael Gil'

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Let $A$ and $\tilde{A}$ be Hilbert--Schmidt operators. For a constant $r>0$, let $i_+(r, A)$ be the number of the eigenvalues of $A$ taken with their multiplicities lying in the half-plane $\{z\in\mathbb{C}: \Re z>r\}$. We suggest the conditions that provide the equality $i_+(r, \tilde{A})=i_+(r, A)$.

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Funct. Approx. Comment. Math., Volume 62, Number 1 (2020), 7-14.

First available in Project Euclid: 9 November 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20] 47B06: Riesz operators; eigenvalue distributions; approximation numbers, s- numbers, Kolmogorov numbers, entropy numbers, etc. of operators
Secondary: 15A18: Eigenvalues, singular values, and eigenvectors 15A69: Multilinear algebra, tensor products

Hilbert--Schmidt operators matrices eigenvalues inertia perturbations


Gil', Michael. An estimate for the number of eigenvalues of a Hilbert--Schmidt operator in a half-plane. Funct. Approx. Comment. Math. 62 (2020), no. 1, 7--14. doi:10.7169/facm/1760.

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