The product formula for regularized Fredholm determinants
Thomas Britz, Alan Carey, Fritz Gesztesy, Roger Nichols, Fedor, Sukochev, and Dmitriy Zanin

TL;DR
This paper derives a product formula for higher regularized Fredholm determinants associated with operators in Schatten classes, extending known formulas from trace and Hilbert--Schmidt cases to more general settings.
Contribution
The paper provides the first explicit product formula for higher regularized Fredholm determinants for operators in Schatten classes beyond the Hilbert--Schmidt case.
Findings
Derived the product formula for ${ m det}_{ ext{H},k}$ for $k eq 2$
Extended the classical product formula to higher regularized determinants
Filled a gap in the literature on Fredholm determinant identities
Abstract
For trace class operators ( a complex, separable Hilbert space), the product formula for Fredholm determinants holds in the familiar form \[ {\det}_{\mathcal{H}} ((I_{\mathcal{H}} - A) (I_{\mathcal{H}} - B)) = {\det}_{\mathcal{H}} (I_{\mathcal{H}} - A) {\det}_{\mathcal{H}} (I_{\mathcal{H}} - B). \] When trace class operators are replaced by Hilbert--Schmidt operators and the Fredholm determinant , , by the 2nd regularized Fredholm determinant , , the product formula must be replaced by \[ {\det}_{\mathcal{H},2} ((I_{\mathcal{H}} - A) (I_{\mathcal{H}} - B)) = {\det}_{\mathcal{H},2}…
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