Archiv der Mathematik

, Volume 91, Issue 6, pp 544–553 | Cite as

On range tripotents in JBW*-triples



Let B be a JBW*-triple, let A be a JB*-subtriple of B and let \({\mathcal{R}}(A)\) be the set of range tripotents relative to A. It is shown that, under certain conditions, the supremum of a family of range tripotents in \({\mathcal{R}}(A)\) coincides with that in the complete lattice \(\tilde{\mathcal{U}}(B)\) of all tripotents in B. As a consequence, a sufficient condition for a tripotent to be a range tripotent relative to A is obtained. The action of isomorphisms on range tripotents is investigated, and an analysis of the suprema of families of spectral range tripotents leads to a generalization of a result known for open projections in W*-algebras.

Mathematics Subject Classification (2000).

Primary 46L70 Secondary 17C65 


JBW*-algebra JB*-triple JBW*-triple open tripotent range tripotent 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  1. 1.Departamento de MatemáticaInstituto Superior Técnico, TU LisbonLisbonPortugal

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