TY  - JOUR
ID  - Bračič2015
LB  - Bračič2015
AU  - Bračič, Janko
AU  - Diogo, Cristina
TI  - Hildebrandt's theorem for the essential spectrum
ST  - Hildebrandt's theorem for the essential spectrum
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2015
VL  - 35
IS  - 3
SP  - 279
EP  - 285
DO  - http://dx.doi.org/10.7494/OpMath.2015.35.3.279
UR  - http://dx.doi.org/10.7494/OpMath.2015.35.3.279
AB  - 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 \(A\).
KW  - essential spectrum
KW  - essential numerical range
KW  - Hildebrandt's theorem
SN  - 1232-9274
ER  -