Topological invariance of the Witten index
The index of an operator A is defined by \(ind(A)=\dim (Ker(A))-\dim (Ker(A\) *)). The Witten index is defined by \[ ind_ t(A)=tr(e^{- tA\quad *A}-e^{-tAA\quad *}). \] It is known that \(ind(A+C)=ind(A)\), if C is compact. It is proved that \[ ind_ t(A+C)=ind_ t(A) \] for a large class of C.
scientific article; zbMATH DE number 4060149
scientific article