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Discussions on partial isometries in Banach spaces and Banach algebras
Abdullah Alahmari,Mohamed Mabrouk,Mohamed Aziz Taoudi 대한수학회 2017 대한수학회보 Vol.54 No.2
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.
DISCUSSIONS ON PARTIAL ISOMETRIES IN BANACH SPACES AND BANACH ALGEBRAS
Alahmari, Abdulla,Mabrouk, Mohamed,Taoudi, Mohamed Aziz Korean Mathematical Society 2017 대한수학회보 Vol.54 No.2
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.