Guillemin Transform and Toeplitz Representations for Operators on Singular Manifolds
Analysis of PDEs
2011-11-08 v1 Functional Analysis
Operator Algebras
Abstract
An approach to the construction of index formulas for elliptic operators on singular manifolds is suggested on the basis of K-theory of algebras and cyclic cohomology. The equivalence of Toeplitz and pseudodifferential quantizations, well known in the case of smooth closed manifolds, is extended to the case of manifolds with conical singularities. We describe a general construction that permits one, for a given Toeplitz quantization of a C^*-algebra, to obtain a new equivalent Toeplitz quantization provided that a resolution of the projection determining the original quantization is given.
Cite
@article{arxiv.math/0503267,
title = {Guillemin Transform and Toeplitz Representations for Operators on Singular Manifolds},
author = {V. Nazaikinskii and G. Rozenblum and A. Savin and B. Sternin},
journal= {arXiv preprint arXiv:math/0503267},
year = {2011}
}
Comments
26 pages