Institute for Mathematical Physics Traces on Algebras of Parameter Dependent Pseudodiierential Operators and the Eta{invariant Traces on Algebras of Parameter Dependent Pseudodiierential Operators and the Eta{invariant
نویسنده
چکیده
We identify Melrose's suspended algebra of pseudodiierential operators with a subalgebra of the algebra of parametric pseudodiierential operators with parameter space R. For a general algebra of parametric pseudodiierential operators, where the parameter space may now be a cone ? 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 Cliiord representations we construct for each rst order elliptic diierential operator a natural family of parametric pseudodiierential operators over R 2k?1. The eta{ invariant of this family coincides with the spectral eta{invariant of the operator.
منابع مشابه
A pr 1 99 8 Traces on algebras of parameter dependent pseudodifferential operators and the eta – invariant
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 ⊂ Rp, we construct a unique “symbol valued trace”, which extends the L2–trace on operators of small order. This a...
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متن کاملTraces on algebras of parameter dependent pseudodifferential operators and the eta–invariant
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 ⊂ Rp, we construct a unique “symbol valued trace”, which extends the L2–trace on operators of small order. This c...
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