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An estimate for the number of eigenvalues of a Hilbert-Schmidt operator in a half-plane. (English) Zbl 07225495
Summary: 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 \(\{z\in\mathbb{C}: \mathfrak{R} z>r\}\). We suggest the conditions that provide the equality \(i_+(r, \tilde{A})=i_+(r, A)\).
MSC:
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
15A18 Eigenvalues, singular values, and eigenvectors
15A69 Multilinear algebra, tensor calculus
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