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 $A^{\ast }(A^{\ast }A-A{A}^{\ast })A\ge 0$, i.e.$\Vert A^{\ast }Ax\Vert \le \Vert A^{2}x\Vert$, for every $x\in H$.