Abstract
We present a criterion for a pair of self-adjoint operators satisfying a cubic relation, linear in one of the operators, to be*-wild. This criterion is formulated in terms of coefficients. In the case where the relation is not*-wild, it has only one-dimensional and two-dimensional irreducible representations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. A. Kruglyak and Yu. S. Samoilenko, “Unitary equivalence of collections of self-adjoint operators,”Funkts. Anal. Prilozhen.,14, Issue 1, 60–62 (1980).
Yu. S. Samoilenko,Spectral Theory of Families of Self-Adjoint Operators, Kluwer, Dordrecht (1990).
A. Yu. Piryatinskaya and Yu. S. Samoilenko, “Wild problems in the theory of representations of*-algebras generated by generatrices and relations,”Ukr. Mat. Zh.,47, No. 1, 70–78 (1995).
V. L. Ostrovskii and Yu. S. Samoilenko, “Representation of*-algebras with two generatrices and polynomial relations,”Zap. Nauch. Sem. Leningr. Otd. Mat. Inst.,179, 121–129 (1989).
V. L. Ostrovskii and Yu. S. Samoilenko, “On pairs of self-adjoint operators,”Seminar Sophus Lie,3, No. 2, 185–218 (1993).
Yu. N. Bespalov, Yu. S. Samoilenko, and V. S. Shul'man, “On collections of operators satisfying semilinear relations,” in:Application of the Methods of Functional Analysis in Mathematical Physics [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1991), pp. 28–51.
S. A. Kruglyak,Representations of Involutory Quivers [in Russian], Deposited at VINITI No. 7266-84, Kiev (1984).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 600–601, May, 1995.
Rights and permissions
About this article
Cite this article
Bagro, O.V. Pairs of self-adjoint operators satisfying a cubic relation. Ukr Math J 47, 694–695 (1995). https://doi.org/10.1007/BF01059042
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01059042