Abstract
Unbounded pairs of self-adjoint operatorsA andB satisfying the algebraic relationF 1(A)B=BF 2(A) are studied. For these relations, various definitions of “integrable” pairs of operators are presented and the class of “tame” relations is indicated; for the “tame” relations, the irreducible pairs are described and a structure theorem is presented.
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V. L. Ostrovskii and Yu. S. Samoilenko, “The families of unbounded self-adjoint operators satisfying the non-Lie relations,”Funkts. Anal. Prilozhen.,23, Issue 2, 67–68 (1989).
V. L. Ostrovskii and Yu. S. Samoilenko, “Unbounded operators satisfying non-Lie commutation relations,”Rep. Math. Phys.,28, No. 1, 91–104 (1989).
Yu. S. Samoilenko,Spectral Theory of Collections of Self-Adjoint Operators, Kluwer Acad. Publ., Dordrecht-Boston-London (1990).
Yu. N. Bespalov, Yu. S. Samoilenko, and V. S. Shul'man, “On the collections of operators satisfying semilinear relations,” in: Applications of the Functional-Analysis Methods in Mathematical Physics [in Russian],Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1991) pp. 28–51.
S. A. Kruglyak and Yu. S. Samoilenko, “On the unitary equivalence of collections of self-adjoint operators,”Funkts. Anal. Prilozhen.,14, Issue 1, 59–62 (1980).
Yu. N. Bespalov and Yu. S. Samoilenko, “Algebraic operators and pairs of self-adjoint operators satisfying polynomial relations,”Funkts. Anal. Prilozhen.,25, Issue 4, 72–74 (1991).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 9, pp. 1253–1258, September, 1993.
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Ostrovskii, V.L., Samoilenko, Y.S. On pairs of unbounded self-adjoint operators satisfying an algebraic relation. Ukr Math J 45, 1406–1412 (1993). https://doi.org/10.1007/BF01058638
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DOI: https://doi.org/10.1007/BF01058638