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 <TEX>$C^*$</TEX>-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 <TEX>$C^*$</TEX>-algebras. Finally, we study the notion of (m, p)-semi partial isometries.
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