The S-spectrum of combinations of idempotents on two-sided quaternionic Banach algebra

• Date: 2026
• Main Authors: Moulaharabbi, Somayya, Barraa, Mohamed
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2026
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8410
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 We establish the relationship between the S-spectrum of $fg$ and the S-spectrum of $\alpha f+\beta g,$ where $f$ and $g$ are two idempotents on a two-sided quaternionic Banach algebra $\mathcal{A}$ and $\alpha, \beta\in\mathbb{R}.$ We  also study the invertibility of linear combinations of...