## Functiones et Approximatio Commentarii Mathematici

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

Michael Gil'

#### Abstract

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 $i_+(r, \tilde{A})=i_+(r, A)$.

#### Article information

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

Dates
First available in Project Euclid: 9 November 2019

https://projecteuclid.org/euclid.facm/1573268425

Digital Object Identifier
doi:10.7169/facm/1760

Mathematical Reviews number (MathSciNet)
MR4074383

Zentralblatt MATH identifier
07225495

#### Citation

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. https://projecteuclid.org/euclid.facm/1573268425

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