Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

Discussions on partial isometries in Banach spaces and Banach algebras

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

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