Representations of relations of the form i [A, B] = f (A) + g (B)
It is proved that all nontrivial representations of quadratic relation i[A, B]=f(A)+g(B) with self-adjoint operators A, B are unbounded if f and g are nonnegative; for any f and g this relation does not have nontrivial finite-dimensional representations and factor-representations of type II1, but can have infinite-dimensional irreducible representations with bounded operators.
English version (Springer): Ukrainian Mathematical Journal 43 (1991), no. 1, pp 91-94.
Citation Example: Samoilenko Yu. S., Shulman V. S. Representations of relations of the form i [A, B] = f (A) + g (B) // Ukr. Mat. Zh. - 1991. - 43, № 1. - pp. 110-114.