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Classification of traces and hypertraces on spaces of classical pseudodifferential operators

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Lesch, Matthias ; Neira-Jiménez, Carolina
Date of publication of this fulltext: 18 Apr 2011 06:46


Let M be a closed manifold and let CL•(M) be the algebra of classical pseudodifferential operators. The aim of this note is to classify trace functionals on the subspaces CLa(M) ⊂ CL•(M) of operators of order a. CLa(M) is a CL0(M)–module for any real a; it is an algebra only if a is a non–positive integer. Therefore, it turns out to be useful to introduce the notions of pretrace and hypertrace. ...


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