Opuscula Math. 35, no. 3 (), 279-285
http://dx.doi.org/10.7494/OpMath.2015.35.3.279
Opuscula Mathematica

# Hildebrandt's theorem for the essential spectrum

Abstract. We prove a variant of Hildebrandt's theorem which asserts that the convex hull of the essential spectrum of an operator $$A$$ on a complex Hilbert space is equal to the intersection of the essential numerical ranges of operators which are similar to $$A$$. As a consequence, it is given a necessary and sufficient condition for zero not being in the convex hull of the essential spectrum of $$A$$.
Keywords: essential spectrum, essential numerical range, Hildebrandt's theorem.
Mathematics Subject Classification: 47A10, 47A12.