Weyl's theorem for algebraically class A operators

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 ker A vertical bar([TH]) = 0 arid 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 vertical bar([TH]) = 0. This leads as to show that a class A operator whose Weyl spectrum equals to zero is always compact and normal.