Opuscula Math. 35, no. 3 (2015), 279-285
http://dx.doi.org/10.7494/OpMath.2015.35.3.279

 
Opuscula Mathematica

Hildebrandt's theorem for the essential spectrum

Janko Bračič
Cristina Diogo

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.

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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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