I have been following the book "Methods of Modern Mathematical Physics I: Functional Analysis - Reed & Simon", and I got some doubts concerning the topics of the book but are not considered in the book.
Given two operators $A$ and $B$ unitary equivalents, this is, there exist an unitary operator $U$ such that $$UAU^{-1}=B.$$ Is it true that $\sigma_{ess}(A)=\sigma_{ess}(B)?$
While it is easy to see that $\sigma(A)=\sigma(B)$, the question considering essential spectrums is not so clear for me.
I would appreciate any help.
Everything mentioned in the definition of essential spectrum is invariant under unitary equivalence, so yes, it is true.