Bull. Korean Math. Soc. 2017; 54(2): 485-495
Online first article March 13, 2017 Printed March 31, 2017
https://doi.org/10.4134/BKMS.b160055
Copyright © The Korean Mathematical Society.
Abdulla Alahmari, Mohamed Mabrouk, and Mohamed Aziz Taoudi
College of Applied Sciences, University of Gab\`es, National School of Applied Sciences
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
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