A new variant of Hildebrandt's theorem for the Weyl spectrum in Banach spaces

Abstract

The main purpose of this paper is to establish a new variant of the  Hildebrandt's theorem for the Weyl spectrum in a separable Banach space. This theorem asserts that the convex hull of
the Weyl spectrum of an operator $T$ is equal to the intersection
of the Weyl numerical spectra  of operators that are similar to $T$.