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Hildebrandt's theorem for the essential spectrum

Bracic J., Diogo C.

Opuscula Mathematica

2015

Vol. 35, no. 3

279--285

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.