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 Discussions on partial isometries in Banach spaces and Banach algebras Bull. Korean Math. Soc. 2017 Vol. 54, No. 2, 485-495 https://doi.org/10.4134/BKMS.b160055Published online March 31, 2017 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. Keywords : $C^*$-algebra, partial isometry, semi-partial isometry MSC numbers : Primary 39B82; Secondary 44B20, 46C05 Downloads: Full-text PDF