On the trace formula for elliptic pseudodifferential operators over \(C^*\)-algebras
type: Item
instance of: scholarly article
title: On the trace formula for elliptic pseudodifferential operators over \(C^*\)-algebras
zbMATH Open document ID: 0587.58051
published in: Moscow University Mathematics Bulletin
publication date: 1984-01-01T00:00:00Z
review text: For a \(C^*\) algebra A, the author considers pseudo-differential operators which act on smooth functions with values in \(A^ n\), the direct product of n copies of A. For such operators he proves a number of results well known for specific \(C^*\) algebras. These include: the existence of an adjoint, the existence of an inverse of an elliptic pseudo-differential operator, the existence of powers of a suitable positive operator and finally the existence of a trace of such powers and identification of its properties. He concludes by remarking that his framework allows one to extend the Atiyah-Bott index formula to such elliptic pseudo-differential operators for \(C^*\) algebras.
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 47Gxx
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 58J40
zbMATH DE Number: 3942576
zbMATH Keywords: pseudo-differential operators
zbMATH Keywords: existence of an adjoint
zbMATH Keywords: existence of an inverse of an elliptic pseudo-differential operator
zbMATH Keywords: powers of a suitable positive operator
zbMATH Keywords: existence of a trace
zbMATH Keywords: Atiyah-Bott index formula
author: Muhammad Aslam Noor
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3942576