Abdulla Alahmari, Mohamed Mabrouk, and Mohamed Aziz Taoudi College of Applied Sciences, University of Gab\`es, National School of Applied Sciences
Abstract : The aim of this paper is twofold. Firstly, we introduce the concept of semi-partial isometry in a Banach algebra and carry out a comparison and a classification study for this concept. In particular, we show that in the context of $C^*$-algebras this concept coincides with the notion of partial isometry. Our results encompass several earlier ones concerning partial isometries in Hilbert spaces, Banach spaces and $C^*$-algebras. Finally, we study the notion of $(m, p)$-semi partial isometries.