a1 Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05315-970 São Paulo, Brazil (email@example.com)
Let us consider the set SA(Rn) of rapidly decreasing functions G: Rn → A, where A is a separable C*-algebra. We prove a version of the Calderón–Vaillancourt theorem for pseudodifferential operators acting on SA(Rn) whose symbol is A-valued. Given a skew-symmetric matrix, J, we prove that a pseudodifferential operator that commutes with G(x + JD), G SA(Rn), is of the form F(x − JD), for F a C∞-function with bounded derivatives of all orders.
(Received October 12 2003)
(Accepted April 06 2005)