Opuscula Mathematica
Opuscula Math. 35, no. 3 (), 279-285
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.
Cite this article as:
Janko Bračič, Cristina Diogo, Hildebrandt's theorem for the essential spectrum, Opuscula Math. 35, no. 3 (2015), 279-285, http://dx.doi.org/10.7494/OpMath.2015.35.3.279
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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