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Traces on algebras of parameter dependent pseudodifferential operators and the eta-invariant | | Matthias Lesch
; Markus J. Pflaum
; | | Date: |
29 Apr 1998 | | Journal: | Trans. Amer. Math. Soc. 352 (2000), No 11, 4911--4936 | | Subject: | Functional Analysis; Differential Geometry; Operator Algebras MSC-class: 58G15 | math.FA math.DG math.OA | | Abstract: | We 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 $GammasubsetR^p$, 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. | | Source: | arXiv, math.FA/9804136 | | Services: | Forum | Review | PDF | Favorites | |
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