On non-adjointable semi-Weyl and semi-B-Fredholm operators over C*-algebras

Abstract

We extend further semi-A-Fredholm theory by generalizing the results from classical semi-Weyl theory on Hilbert spaces. Moreover, we obtain an analogue of the results from [17] in the setting of non-adjointable operators. Finally, we provide several examples on semi-A-Fredholm and semi- A-Weyl operators over a unital C*-algebra A. We give also the examples of semi-A-Fredholm operators with non-closed image