B-Fredholm elements in primitive C*-algebras

Abstract

Let A{\mathcal{A}} be a unital primitive C∗\ast -algebra. This article studies the properties of the B-Fredholm elements, the B-Weyl elements and the B-Browder elements in A{\mathcal{A}}. Particularly, this article describes the B-Fredholm element as the sum of a Fredholm element and a nilpotent element. In addition, the socle of A{\mathcal{A}} is characterized by the B-Fredholm elements.

Keywords

• primitive c*-algebra
• b-fredholm elements
• b-browder elements
• socle
• 16d60
• 46h99
• 47a05
• 47a10
• 47a53