Traces on algebras of parameter dependent pseudodifferential operators and the eta–invariant Journal Article uri icon

Overview

abstract

  • We identify Melrose’s suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space ; ; ; ; R; ; mathbb {R}; ; ; . For a general algebra of parametric pseudodifferential operators, where the parameter space may now be a cone ; ; ; ; Γ; ; ; ; R; ; p; ; ; Gamma subset mathbb {R}^p; ; ; , we construct a unique “symbol valued trace”, which extends the ; ; ; ; L; 2; ; L^2; ; ; –trace on operators of small order. This construction is in the spirit of a trace due to Kontsevich and Vishik in the nonparametric case. Our trace allows us to construct various trace functionals in a systematic way. Furthermore, we study the higher–dimensional eta–invariants on algebras with parameter space ; ; ; ; ; R; ; ; 2; k; ; 1; ; ; mathbb {R}^{2k-1}; ; ; . Using Clifford representations we construct for each first order elliptic differential operator a natural family of parametric pseudodifferential operators over ; ; ; ; ; R; ; ; 2; k; ; 1; ; ; mathbb {R}^{2k-1}; ; ; . The eta–invariant of this family coincides with the spectral eta–invariant of the operator.

publication date

  • January 1, 2000

Date in CU Experts

  • September 19, 2013 11:32 AM

Full Author List

  • Lesch M; Pflaum M

author count

  • 2

Other Profiles

International Standard Serial Number (ISSN)

  • 0002-9947

Electronic International Standard Serial Number (EISSN)

  • 1088-6850

Additional Document Info

start page

  • 4911

end page

  • 4936

volume

  • 352

issue

  • 11