Functional calculus and joint torsion of pairs of almost commuting operators

2014/09/22 by Joseph Migler, Migler, Joseph
Mathematics · #47A53 #47A60 #47B35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Holomorphic and Operator Theory #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Primary 19C20 #Secondary 47A13 #math.KT #math.OA #msc:19C20 #msc:47A13 #msc:47A53 #msc:47A60 #msc:47B35

paper · pdf · doi:10.48550/arxiv.1409.6289

27 pages

arxiv created 2014/09/22 · openalex publication_date 2014/09/22 · arxiv updated 2014/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates the transformation of determinants of pairs of Fredholm operators with trace class commutators. We study the extent to which the functional calculus commutes, modulo operator ideals, with projections in a finitely summable Fredholm module. As an application, we recover in particular some results of R. Carey and J. Pincus on determinants and Tate tame symbols. Additionally, we obtain variational formulas for joint torsion.

Related

• Joint torsion equals the determinant invariant
• Joint torsion of several commuting operators
• Almost commuting functions of almost commuting self-adjoint operators
• Functions of almost commuting operators and an extension of the Helton-Howe trace formula
• Torsion modules and differential operators in infinitely many variables