The Calderon projection over C* algebras

TL;DR

This paper extends the Calderon projection concept to twisted Dirac operators on manifolds with boundary within the framework of C*-algebras, utilizing the Mischenko--Fomenko calculus and constructing an invertible double.

Contribution

It introduces a novel construction of the Calderon projection and invertible double for twisted Dirac operators on C*-Hilbert modules, generalizing classical results.

Findings

Constructed Calderon projection for twisted Dirac operators.

Developed the Mischenko--Fomenko pseudodifferential calculus in this context.

Established the existence of an invertible double generalizing classical theory.

Abstract

We construct the Calderon projection on the space of Cauchy datas for a twisted Dirac operator in the Mischenko--Fomenko pseudodifferential calculus for operators acting on bundles of finitely generated $C^*$--Hilbert modules on a compact manifold with boundary. In particular an invertible double is constructed generalizing the classical result.