Abstract
We prove a criterion for nuclearity of a linear operator and establish the form of the greatest two-sided ideal of the set of all compact Akhiezer integral operators in L 2 and the set of all Akhiezer integral operators in L 2.
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References
Akhiezer N. I. and Glazman I. M., The Theory of Linear Operators in Hilbert Space [in Russian], Nauka, Moscow (1966).
Korotkov V. B., “A nuclearity criterion for linear operators,” Siberian Math. J., 39, No.3, 484–487 (1998).
Korotkov V. B., An Introduction to Algebraic Theory of Integral Operators [in Russian], Kolorit, Vladivostok (2000).
Korotkov V. B., Integral Operators [in Russian], Nauka, Novosibirsk (1983).
Kato T., Perturbation Theory for Linear Operators [Russian translation], Mir, Moscow (1972).
Pietsch A., Operator Ideals [Russian translation], Mir, Moscow (1982).
Nikishin E. M., “Resonance theorems and sublinear operators,” Uspekhi Mat. Nauk, 25, No.6, 129–191 (1970).
Korotkov V. B., “On algebraic properties of Akhiezer integral operators,” Siberian Math. J., 38, No.3, 488–491 (1997).
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Original Russian Text Copyright © 2005 Korotkov V. B.
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 1072–1078, September– October, 2005.
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Korotkov, V.B. One Criterion for Nuclearity of Linear Operators. Sib Math J 46, 857–862 (2005). https://doi.org/10.1007/s11202-005-0083-1
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DOI: https://doi.org/10.1007/s11202-005-0083-1