Abstract

In [5], Harte used the well-known Atkinson’s theorem (which gives a necessary and sufficient condition for a Banach space operator to be Fredholm) to introduce a Fredholm theory relative to an arbitrary Banach algebra homomorphism. In [2], Berkani defined the notion of a B-Fredholm operator - a type of generalized Fredholm operator - for which an Atkinson-type theorem was established in [3] and utilized in [4] to introduce B-Fredholm theory in general Banach algebras. In this talk we will discuss two extensions of Harte’s Fredholm theory, namely B-Fredholm theory and generalized B-Fredholm theory (in short, GB-Fredholm theory), which unify Harte’s Fredholm theory with Drazin and Koliha-Drazin invertibility, respectively.

References
   [1] R. Benjamin and J. Aliyu (2026). More on (generalized) B-Fredholm theory in general Banach algebras. Filomat, 849-864.
   [2] M. Berkani (1999). On a class of quasi-Fredholm operators. Integr. Equ. Oper. Theory, 244-249.
   [3] M. Berkani and M. Sarih (2001). An Atkinson-type theorem for B-Fredholm operators. Studia Math., 251-257.
   [4] M. Cvetković, E. Boasso, and S. Živković-Zlatanović (2016). Generalized B-Fredholm Banach algebra elements. Mediterr. J. Math., 3729–3746.
   [5] R. Harte (1982). Fredholm theory relative to a Banach algebra homomorphism. Math. Z., 431–436.

Speaker: Prof. Ronalda Benjamin | Department of Mathematics  |  Stellenbosch University

Chairperson: Prof. Ralph Agyei Twum | Department of Mathematics | University of Ghana 

Meeting ID: 326 260 537 811 960 | Passcode: 7xe6Mg2N | Teams: Link 

All are cordially invited.

Bio

Dr. Ronalda Benjamin is a Senior Lecturer in the Department of Mathematical Sciences at Stellenbosch University, where she obtained her PhD in Mathematics in 2016. Her area of specialization is Functional Analysis, with a particular focus on Fredholm theory in general (ordered) Banach algebras. She is also a member of the Functional Analysis Steering Committee, which coordinates functional analysis activities in South Africa, including the FAOTSA (Functional Analysis and Operator Theory South Africa) workshops.