On pairs of unbounded self-adjoint operators satisfying an algebraic relation

Abstract

Unbounded pairs of self-adjoint operators A andB satisfying the algebraic relation F 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.