Functional Analysis and Applications Seminar 

20/06/2008, 15:00 — 16:00 — Room P3.10, Mathematics Building
Lina Oliveira, Instituto Superior Técnico, U.T. Lisboa

Range tripotents and order

The partial order relation existing in the set of tripotents $U(B)$ in a $\mathrm{JBW}$*-triple $B$ is such that it suffices to adjoin a greatest element for the new set to become a complete lattice. For example, such is the case of the partial isometries in a $W$*-algebra which, as it is well-known, are exactly the tripotents in the algebra. Any $\mathrm{JB}$*-subtriple $A$ of $B$ determines a subset $R(A)$ of tripotents called the range tripotents relative to $A$. It is the aim of this talk to present new results concerning the restricted partial order relation in $R(A)$. Furthermore, an analysis of the suprema of families of range tripotents will lead to establishing a counterpart of a result already existing for projections in $W$*-algebras. It is intended to provide the background material needed to make the talk understandable to an audience familiar with operator algebras.