Boundedness of Pseudodifferential Operators of C^*-Algebra-Valued Symbol

Details Boundedness of Pseudodifferential Operators of C^*-Algebra-Valued Symbol Boundedness of Pseudodifferential Operators of C^*-Algebra-Valued Symbol

2003-10-03

arxiv.org/abs/math/0310037v2

Mathematics

Operator Algebras

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Scientific paper

Let us consider the set S^A(\R^n) of rapidly decreasing functions G:\R^n \to A, where A is a separable C^*-algebra. We prove a version of the Calder\'on-Vaillancourt theorem for pseudodifferential operators acting on S^A(\R^n) whose symbol is A-valued. Given a skew-symmetric matrix, J, we prove that a pseudodifferential operator that commutes with G(x+JD), G\in S^A(\R^n), is of the form F(x-JD), for F a C^\infty-function with bounded derivatives of all orders.

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