Pseudodifferential analysis on continuous family groupoids
type: Item
instance of: scholarly article
title: Pseudodifferential analysis on continuous family groupoids
zbMATH Open document ID: 0961.22005
author: Robert Lauter
author: Bertrand Monthubert
author: Victor Nistor
published in: Documenta Mathematica
publication date: 2000-12-12T00:00:00Z
full work available at URL: https://eudml.org/doc/120940
full work available at URL: 19.html
review text: Summary: We study properties and representations of the convolution algebra and the algebra of pseudodifferential operators associated to a continuous family groupoid. We show that the study of representations of the algebras of pseudodifferential operators of order zero completely reduces to the study of the representations of the ideal of regularizing operators. This recovers the usual boundedness theorems for pseudodifferential operators of order zero. We prove a structure theorem for the norm completions of these algebras associated to groupoids with invariant filtrations. As a consequence, we obtain criteria for an operator to be compact or Fredholm. We end with a discussion of the significance of these results to the index theory of operators on certain singular spaces. For example, we give a new approach to the question of the existence of spectral sections for operators on coverings of manifolds with boundary. We expect that our results will also play a role in the analysis on more general singular spaces.
Mathematics Subject Classification ID: 22A22
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 58H05
Mathematics Subject Classification ID: 58J22
Mathematics Subject Classification ID: 58J40
zbMATH DE Number: 1542672
zbMATH Keywords: index theory
zbMATH Keywords: compact and Fredholm operators
zbMATH Keywords: convolution algebra
zbMATH Keywords: algebra of pseudodifferential operators
zbMATH Keywords: continuous family groupoid
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1542672