A pr 1 99 8 Traces on algebras of parameter dependent pseudodifferential operators and the eta – invariant
نویسندگان
چکیده
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 allows to construct various trace functionals in a systematic way. Furthermore we study the higher–dimensional eta–invariants on algebras with parameter space R2k−1. Using Clifford representations we construct for each first order elliptic differential operator a natural family of parametric pseudodifferential operators over R2k−1. The eta– invariant of this family coincides with the spectral eta–invariant of the operator. 1991 Mathematics Subject Classification. 58G15
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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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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 al...
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