C*-Algebra-valued-symbol pseudodifferential operators: abstract characterizations

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dc.creatorMelo, Severino T.
dc.creatorMerklen, Marcela I.
dc.date2006-10-11
dc.date2006-10-13
dc.date.accessioned2026-07-07T07:28:58Z
dc.date.available2026-07-07T07:28:58Z
dc.descriptionGiven a separable unital C*algebra $C$, let $E_n$ denote the Hilbert module equal to the completion of the Schwartz space of rapidly decreasing smooth functions from $R^n$ to $C$ equipped with the $C$-valued inner product given by integration. Let $B$ denote the space of all smooth functions with bounded derivatives from $R^n$ to $C$. For each $a$ in $B$, let $O(a)$ denote the pseudodifferential operator of symbol $a$. $O$ maps $B$ to $H$, the set of all adjointable operators on $E_n$ which have smooth orbit under the canonical action of the Heisenberg group. We construct a left inverse for $O$, $S:H\to B$, and prove that $S$ is an inverse for $O$ if $C$ is commutative. The case when $C$ is the complex numbers was proven by Cordes in 1979. As a consequence, we prove, for commutative separable unital C*algebras, a characterization of a certain class of pseudodifferential operators conjectured by Rieffel in 1993.
dc.descriptionA few misprints have been corrected
dc.identifierhttps://arxiv.org/abs/math/0610378
dc.identifierhttp://arxiv.org/abs/math/0610378
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117930
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.subject47G30; 46L65; 35S05
dc.titleC*-Algebra-valued-symbol pseudodifferential operators: abstract characterizations
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