Trace formula for almost Lie algebra of operators
type: Item
instance of: scholarly article
title: Trace formula for almost Lie algebra of operators
zbMATH Open document ID: 0616.46063
DOI: 10.1007/BF01213795
published in: Integral Equations and Operator Theory
publication date: 1985-01-01T00:00:00Z
review text: A linear subspace of the algebra of all bounded linear operators on a Hilbert space is called an almost Lie algebra if it is a Lie algebra modulo the trace class operators. This object is mapped via a natural homomorphism to a Lie algebra. By choosing a basis in this Lie algebra, a bilinear functional on the enveloping algebra of this Lie algebra is defined through the trace of some operators which are related to the commutators. A general trace formula is obtained by means of the partial derivatives and symmetry operation in the enveloping algebra. Certain special cases with more structure are analyzed. This work is related to work of Carey and Pincus, as well as to the work of Helton and Howe. It is mentioned at the end of the paper that this work is related to the Connes cyclic cohomology.
Mathematics Subject Classification ID: 46L70
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 17B35
zbMATH DE Number: 3998544
zbMATH Keywords: trace formula
zbMATH Keywords: almost Lie algebra
zbMATH Keywords: Lie algebra modulo the trace class operators
zbMATH Keywords: enveloping algebra
zbMATH Keywords: Connes cyclic cohomology
author: Daoxing Xiao
reviewed by: Martin E. Walter
MaRDI profile type: Publication
Wikidata QID: Q115393896
cites work: Q3213739
cites work: Traces of commutators of integral operators
cites work: Mosaic and principal function of hyponormal and semi-hyponormal operators
cites work: Quantized differential forms
cites work: Spectral theory of hyponormal operators
cites work: On unitary interpolants and Fredholm infinite block Toeplitz matrices
full work available at URL: https://doi.org/10.1007/bf01213795
OpenAlex ID: W2089282260
description: scientific article; zbMATH DE number 3998544