On New Approach to semi-Fredholm theory in unital C*-algebras (2308.12070v1)

Abstract: Axiomatic Fredholm theory in unital C*-algebras was established by Keckic and Lazovic in [15]. Following the purely algebraic approach by Keckic and Lazovic, in [14] we extended further this theory to axiomatic semi-Fredholm and semi-Weyl theory in unital C*-algebras. However, recently, in [11] we developed another approach to axiomatic Fredholm theory in unital C*-algebras which is based on the theory of Hilbert modules and which is equivalent to the algebraic approach by Keckic and Lazovic. In this paper, we extend further this new Hilbert-module approach from Fredholm theory to semi-Fredholm and semi-Weyl theory in unital C*-algebras. Hence, we provide a new proof of the results in [14].