Continuity of the essential spectrum in the class of quasihyponormal operators

Abstract

Let $H$ be a separable Hilbert space. We write $\sigma (A)$ for the spectrum of $A\in B(H)$, $\sigma_w(A)$ for the Weyl spectrum and $\sigma_b(A)$ for the Browder spectrum. Operator $A\in B(H)$ is quasihyponormal if $A^*(A^*A-AA^*)A\ge 0$, i.e.$\| A^*Ax\|\le \|A^2x\|$, for every $x\in H$.