Almost commuting functions of almost commuting self-adjoint operators

作者：Aleksandrov Aleksei^*; Peller Vladimir

来源：Comptes Rendus Mathematique, 2015, 353(7): 583-588.

DOI：10.1016/j.crma.2015.04.012

Let A and B be almost commuting (i.e. AB - BA is an element of S-1) self-adjoint operators: We construct a functional calculus phi bar right arrow phi(A, B) for phi in the Besov class B-infinity,1(1) (R-2). This functional calculus is linear, the operators phi(A, B) and psi(A, B) almost commute for phi, psi is an element of B-infinity,1(1) (R-2), phi(A, B) = u(A) v (B) whenever phi(s, t) = u(s)v(t), and the Helton-Howe trace formula holds. The main tool is triple operator integrals.

• 出版日期2015-7