Einladung zum Oberseminar Analysis am 15.01.2026

Im Oberseminar Analysis hält

Dr. Ronalda Benjamin (Stellenbosch University, Department of Mathematical Sciences)

einen Vortrag zum Thema

(Generalized) B-Fredholm theory relative to unital homomorphisms

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 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. More on (generalized) B-Fredholm theory in general Banach algebras. To appear in Filomat.
[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 BFredholm Banach algebra elements. Mediterr. J. Math., 3729–3746.
[5] R. Harte (1982). Fredholm theory relative to a Banach algebra homomorphism. Math. Z., 431–436.


Datum: Donnerstag, 15. Januar 2026
Zeit:       16:40 Uhr
Raum:   WIL A 124

Kontakt: PD Dr. Anke Kalauch

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