2019
Том 71
№ 11

All Issues

Shulman V. S.

Articles: 1
Article (Ukrainian)

Representations of relations of the form i [A, B] = f (A) + g (B)

Samoilenko Yu. S., Shulman V. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 1. - pp. 110-114

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.