Trace formula for almost Lie algebra of operators
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.
Lie algebra modulo the trace class operators
scientific article; zbMATH DE number 3998544