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

TL;DR

This paper introduces a new proof-based approach to axiomatic Fredholm theory in unital C*-algebras, building on and equivalent to previous frameworks but offering fresh insights inspired by Mishchenko and Fomenko.

Contribution

It provides alternative proofs for existing Fredholm theory in unital C*-algebras, enhancing understanding and potentially simplifying the theoretical framework.

Findings

Equivalent to Keckic and Lazovic's approach

New proofs inspired by Mishchenko and Fomenko

Strengthens the theoretical foundation of Fredholm theory

Abstract

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.