On New Approach to Fredholm theory in unital C*-algebras

Motivated by the Fredholm theory on the standard Hilbert module over an unital C*-algebra introduced by Mishchenko and Fomenko, we provide a new approach to axiomatic Fredholm theory in unital C*-algebras established by Keckic and Lazovic in [28]. Our approach is equivalent to the approach introduced by Keckic and Lazovic, however, we provide new proofs which are motivated by the proofs given by Mishchenko and Fomenko.