Trace Class Properties of Resolvents of Callias Operators

We present conditions for a family \(\left(A\left(x\right)\right)_{x\in\mathbb{R}^{d}}\) of self-adjoint operators in \(H^{r}=\mathbb{C}^{r}\otimes H\) for a separable complex Hilbert space \(H\), such that the Callias operator \(D=ic\nabla+A\left(X\right)\) satisfies that \(\left(D^{\ast}D+1\right)...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Author Fürst, Oliver
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.11.2022
Subjects
Hilbert space
Multiplication
Operators
Online AccessGet full text

Cover

More Information
Summary:We present conditions for a family \(\left(A\left(x\right)\right)_{x\in\mathbb{R}^{d}}\) of self-adjoint operators in \(H^{r}=\mathbb{C}^{r}\otimes H\) for a separable complex Hilbert space \(H\), such that the Callias operator \(D=ic\nabla+A\left(X\right)\) satisfies that \(\left(D^{\ast}D+1\right)^{-N}-\left(DD^{\ast}+1\right)^{-N}\) is trace class in \(L^2\left(\mathbb{R}^{d},H^{r}\right)\). Here, \(c\nabla\) is the Dirac operator associated to a Clifford multiplication \(c\) of rank \(r\) on \(\mathbb{R}^{d}\), and \(A\left(X\right)\) is fibre-wise multiplication with \(A\left(x\right)\) in \(L^2\left(\mathbb{R}^{d},H^{r}\right)\).
ISSN:2331-8422