Korotkov, Vitaliĭ Borisovich On unbounded integral operators with quasisymmetric kernels. (Russian. English summary) Zbl 1463.45058 Vladikavkaz. Mat. Zh. 22, No. 2, 18-23 (2020). Summary: In 1935 von Neumann established that a limit spectrum of self-adjoint Carleman integral operator in \(L_2\) contains 0. This result was generalized by the author on nonself-adjoint operators: the limit spectrum of the adjoint of Carleman integral operator contains 0. Say that a densely defined in \(L_2\) linear operator \(A\) satisfies the generalized von Neumann condition if 0 belongs to the limit spectrum of adjoint operator \(A^{\ast}\). Denote by \(B_0\) the class of all linear operators in \(L_2\) satisfying a generalized von Neumann condition. The author proved that each bounded integral operator, defined on \(L_2\), belongs to \(B_0\). Thus, the question arises: is an analogous assertion true for all unbounded densely defined in \(L_2\) integral operators? In this note, we give a negative answer on this question and we establish a sufficient condition guaranteeing that a densely defined in \(L_2\) unbounded integral operator with quasisymmetric lie in \(B_0\). MSC: 45P05 Integral operators 47B34 Kernel operators Keywords:closable operator; integral operator; kernel of an integral operator; limit spectrum; linear integral equation of first or second kind PDF BibTeX XML Cite \textit{V. B. Korotkov}, Vladikavkaz. Mat. Zh. 22, No. 2, 18--23 (2020; Zbl 1463.45058) Full Text: DOI MNR OpenURL References: [1] Korotkov V. B., “On Some Properties of Partially Integral Operators”, Dokl. Akad. Nauk SSSR, 217:4 (1974), 752-754 (in Russian) · Zbl 0302.47038 [2] Korotkov V. B., Integral Operators, Izd-vo Novosib. Gos. Un-ta, Novosibirsk, 1977, 68 pp. (in Russian) [3] Halmos P. R., Sunder V. S., Bounded Integral Operators on \(L^2\) Spaces, Springer Verlag, Berlin-Heidelberg-New York, 1978, 134 pp. · Zbl 0389.47001 [4] Korotkov V. B., “On One Class of Linear Operators in \(L_2\)”, Siberian Mathematical Journal, 60:1 (2019), 89-92 · Zbl 07079963 [5] Korotkov V. B., Integral Operators, Nauka, Novosibirsk, 1983, 224 pp. (in Russian) [6] Korotkov V. B., “On Partially Measure Compact Unbounded Linear Operators in \(L_2\)”, Vladikavkaz. Math. J., 18:1 (2016), 36-41 (in Russian) · Zbl 1474.47054 [7] Korotkov V. B., “Integral Equations of the Third Kind with Unbounded Operators”, Siberian Mathematical Journal, 58:2 (2017), 255-263 · Zbl 1372.45002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.