Weyl’s theorem for algebraically class: a Operators

Abstract

Let A be a bounded linear operator acting on a Hilbert space H. In [32], A. Uchiyama proved that Weyl’s theorem holds for class A operators with the additional condition that kerA|[TH] = 0 and he showed that every class A operator whose Weyl spectrum equals to zero is compact and normal. In this paper we show that Weyl’s theorem holds for algebraically class A operator without the additional condition ker A|[TH] = 0. This leads as to show that a class A operator whose Weyl spectrum equals to zero is always compact and normal.