Lecture Details
Name: Antonio M. Peralta (Universidad de Granada)Speaking: Fri 10th May 09:30 - 09:55Title: Markushevich bases and projectional skeletons for JBW*-triple predualsAbstract: We shall present some new studies on the Banach space underlying the predual, $M_*$, of a JBW$^*$-triple $M$. The new advances show how the algebraic structure of $M$ can be naturally applied to address the question whether $M_*$ is a $1$-Plichko space (i.e., it admits a countably $1$-norming Markushevich basis). A stronger property holds in case $M$ is $\sigma$-finite, because $M_*$ is even weakly compactly generated. The new results extend, to the triple setting, previous conclusions for $L^1$-spaces, preduals of von Neumann algebras, and preduals of JBW$^*$-algebras.