Some spectral quasisimilarity invariants for operators Ciprian FoiasCarl PearcyLarry Smith 47A65spectrumquasisimilarity Let $T$ be a (bounded, linear) operator on a separable, infinite dimensional, complex Hilbert space, and let $q_{\ell re}(T)$ denote the intersection of all the sets $\sigma_{\ell re}(S)$, the intersection of the left and right essential spectra of $S$, where $S$ is quasisimilar to $T$. The main result of this note is that $q_{\ell re}(T)$ is always nonempty. This result contains earlier theorems due to Fialkow [L.A. Fialkow, \textit{A note on quasisimilarity of operators}, Acta Sci. Math. (Szeged) \textbf{39} (1977), 67--85; L.A. Fialkow, \textit{A note on quasisimilarity. II}, Pacific J. Math. \textbf{70} (1977), 151--162], L. Williams [L. Williams, \textit{Doctoral Thesis}, Univ. of Michigan, 1977], Stampfli [J.G. Stampfli, \textit{Quasisimilarity of operators}, Proc. Roy. Irish Acad. Sect. A \textbf{81} (1981), 109--119], and Herrero [D.A. Herrero, \textit{On the essential spectra of quasisimilar operators}, Canad. J. Math. \textbf{40} (1988), 1436--1457]. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.4474 10.1512/iumj.2010.59.4474 en Indiana Univ. Math. J. 59 (2010) 2139 - 2154 state-of-the-art mathematics http://iumj.org/access/