Boundedness of pseudodifferential operators of a C*-algebra-valued symbol
Published online by Cambridge University Press: 12 July 2007
Abstract
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.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 6 , December 2005 , pp. 1279 - 1286
- Copyright
- Copyright © Royal Society of Edinburgh 2005
- 1
- Cited by