On Kitaev's determinant formula

TL;DR

This paper identifies a specific condition ensuring that the determinant of the commutator of two invertible operators equals one, contributing to the understanding of operator determinants in functional analysis.

Contribution

It provides a new sufficient condition for the determinant of the commutator of two invertible operators to be equal to one.

Findings

Established a sufficient condition for det(ABA^{-1}B^{-1})=1

Enhanced understanding of determinants in operator theory

Potential applications in functional analysis and quantum mechanics

Abstract

We establish a sufficient condition under which ${\rm det}\,(ABA^{-1}B^{-1})=1$ for a pair of bounded, invertible operators $A,B$ on a Hilbert space.