Traces on algebras of parameter dependent pseudodifferential operators and the eta-invariant

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dc.creatorLesch, Matthias
dc.creatorPflaum, Markus J.
dc.date1998-04-29
dc.date1999-02-18
dc.date.accessioned2026-07-07T06:21:28Z
dc.date.available2026-07-07T06:21:28Z
dc.descriptionWe identify Melrose's suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space $\R$. For a general algebra of parametric pseudodifferential operators, where the parameter space may now be a cone $Γ\subset\R^p$, we construct a unique ``symbol valued trace'', which extends the $L^2$-trace on operators of small order. This allows to construct various trace functionals in a systematic way. Furthermore we study the higher-dimensional eta-invariants on algebras with parameter space $\R^{2k-1}$. Using Clifford representations we construct for each first order elliptic differential operator a natural family of parametric pseudodifferential operators over $\R^{2k-1}$. The eta-invariant of this family coincides with the spectral eta-invariant of the operator.
dc.description29 pages, LaTeX2e, revised version of 21 Oct 1998, some minor errors corrected, to appear in Trans. Amer. Math. Soc
dc.identifierhttps://arxiv.org/abs/math/9804136
dc.identifierhttp://arxiv.org/abs/math/9804136
dc.identifierTrans. Amer. Math. Soc. 352 (2000), No 11, 4911--4936
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95609
dc.subjectFunctional Analysis
dc.subjectDifferential Geometry
dc.subjectOperator Algebras
dc.subject58G15
dc.titleTraces on algebras of parameter dependent pseudodifferential operators and the eta-invariant
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