On a perturbation determinant for accumulative operators

TL;DR

This paper develops exponential representations and trace formulas for the perturbation determinant of accumulative operators under purely imaginary sign-definite perturbations, enhancing understanding of spectral properties in complex analysis.

Contribution

It introduces new exponential representations and trace formulas for perturbation determinants of accumulative operators with purely imaginary sign-definite perturbations.

Findings

Derived exponential representations in upper and lower half-planes.

Established trace formulas relating to the perturbation determinant.

Enhanced spectral analysis tools for accumulative operators.

Abstract

For a purely imaginary sign-definite perturbation of a self-adjoint operator, we obtain exponential representations for the perturbation determinant in both upper and lower half-planes and derive respective trace formulas.