Abstract
The question about commutative properties of the singularly perturbed self-adjoint operators arises in connection with the development of the quantum field theory. It is often necessary to know when a pair of unbounded closed self-adjoint commutative operators commute also if one of them or both were replaced by singularly perturbed operators i.e. by operators coinciding with the given operators on a dense subspace. The necessary and sufficient conditions under which the singularly perturbed self-adjoint operators commute are investigated in this note. This research may be applied to the theory of the singularly perturbed normal operators.
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© 1996 Springer Science+Business Media Dordrecht
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Dudkin, N. (1996). The Commutativity of the Singularly Perturbed Self-Adjoint Operators. In: de Monvel, A.B., Marchenko, V. (eds) Algebraic and Geometric Methods in Mathematical Physics. Mathematical Physics Studies, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0693-3_22
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DOI: https://doi.org/10.1007/978-94-017-0693-3_22
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