Traces on algebras of parameter dependent pseudodifferential operators and the eta-invariant
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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 $Γ\subset\R^p$, 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.
29 pages, LaTeX2e, revised version of 21 Oct 1998, some minor errors corrected, to appear in Trans. Amer. Math. Soc
29 pages, LaTeX2e, revised version of 21 Oct 1998, some minor errors corrected, to appear in Trans. Amer. Math. Soc