@Article{Bračič2015,
author = "Bračič, Janko and Diogo, Cristina",
title = "Hildebrandt's theorem for the essential spectrum",
journal = "Opuscula Math.",
year = "2015",
volume = "35",
number = "3",
pages = "279--285",
doi = "http://dx.doi.org/10.7494/OpMath.2015.35.3.279",
url = "http://dx.doi.org/10.7494/OpMath.2015.35.3.279",
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",
issn = "1232-9274"
}