The Weyl calculus and commutativity for systems of selfadjoint matrices (Q689657)

Let \(A= (A_ 1,\dots, A_ n)\) be an \(n\)-tuple of selfadjoint operators in a finite-dimensional Hilbert space. The author characterizes pairwise commutativity of \(A_ 1,\dots,A_ n\) (a purely algebraic notion) in terms of properties of the spectral distribution \(T(A)\) given by the Weyl calculus for \(A\) (a purely analytic property).