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In a JBW*-triple, i.e., a symmetric complex Banach space possessing a predual, the set of tripotents is naturally endowed with a partial order relation. This work is mainly concerned with this partial order relation when restricted to the subset 𝓡(A) of tripotents in a JBW*-triple B formed by the range tripotents of the elements of a JB*-subtriple A of B. The aim is to present recent developments obtained for the poset 𝓡(A) of the range tripotents relative to A, whilst also providing the necessary...
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