Characterizations of tripotents in JB*-triples - Hügli, Remo V. (MATHEMATICA SCANDINAVICA, 2006)
The set $\mathcal{U}(A)$ of tripotents in a $JB^*$-triple $A$ is characterized in various ways. Some of the characterizations use only the norm-structure of $A$. The partial order on $\mathcal{U}(A)$ as well as $σ$-finiteness of tripotents are described intrinsically in terms of the facial structure of the unit ball $A_1$ in $A$, i.e. without reference to the (pre-)dual of $A$. This extends similar results obtained in [6] and simplifies the metric characterization of partial isometries in $C^*$-algebras found in [1](cf. [8].