Citation:
BOUYELLI ANTAR, MENNOUNI ABDELAZIZ. INVESTIGATING THE EXTENDED SPECTRUM: OPERATOR GROUP INVERSE AND DRAZIN INVERSE. Asia Pacific Journal of Mathematics [Internet]. 2025;12 (85).
Abstract:
This paper investigates the relationship between the extended spectrum of a bounded linear operator and its group inverse. We also establish a connection between the extended spectrum of the bounded linear operator and that of its Drazin inverse. As part of our analysis, we prove the following equality: σext((BA)D) = σext((AB)D), where (BA)D and (AB)D represent the Drazin inverses of BA and AB, respectively. 2020 Mathematics Subject Classification. 35K15; 35K55; 35K65; 35B40. Key words and phrases. extended spectrum; operator group inverse; Drazin inverse.