The K-theory of bisingular pseudodifferential algebras

TL;DR

This paper computes the K-theory of C*-algebras formed by the norm-closure of bisingular pseudodifferential operators, providing explicit results for the global calculus in flat Euclidean spaces.

Contribution

It offers the first explicit K-theory calculations for bisingular pseudodifferential operator algebras in the flat case.

Findings

K-theory computed for bisingular pseudodifferential algebras

Results apply to the global calculus in flat Euclidean spaces

Provides a foundation for further analysis of these operator algebras

Abstract

In this paper we calculate the K-theory of $C^{\ast}$-algebras given by the norm-closures of spaces of bisingular pseudodifferential operators. We obtain results for the \emph{global} bisingular calculus in the flat ($\Rr^{n_1 + n_2}$) case.