On Schatten-von Neumann class properties of pseudo-differential operators. Cordes' lemma
Abstract
We prove an extended version of Cordes' lemma concerning trace-class properties of some special pseudo-differential operators. This version of Cordes' lemma is used to improve the results in \cite{Arsu} concerning the Schatten-class properties of pseudo-differential operators in the
(X,τ)
-quantization. Here
X
is an
n
dimensional vector space and
τ
is an endomorphism of
X
.