Essential Spectra of Elementary Operators
L. A. Fialkow · Transactions of the American Mathematical Society · 1981
This paper describes the essential spectrum and index function of the operator $X \to AXB$, where $A$, $B$, and $X$ are Hilbert space operators. Analogous results are given for the restriction of this operator to a norm ideal and partial analogues are given for sums of such operators and for the case when the operators act on a Banach space.