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08 February 2025
 
  » arxiv » 1609.0274

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Preduals of JBW$^*$-triples are 1-Plichko spaces
Martin Bohata ; Jan Hamhalter ; Ondrej F.K. Kalenda ; Antonio M. Peralta ; Hermann Pfitzner ;
Date 1 Sep 2016
AbstractWe prove that the predual, $M_*$, of a JBW$^*$-triple $M$ is a 1-Plichko space (i.e. it admits a countably 1-norming Markushevich basis or, equivalently, it has a commutative 1-projectional skeleton), and obtain a natural description of the $Sigma$-subspace of $M$. This generalizes and improves similar results for von Neumann algebras and JBW$^*$-algebras. Consequently, dual spaces of JB$^*$-triples also are 1-Plichko spaces. We also show that $M_*$ is weakly Lindel"{o}f determined if and only if $M$ is $sigma$-finite if and only if $M_*$ is weakly compactly generated. Moreover, contrary to the proof for JBW$^*$-algebras, our proof dispenses with the use of elementary submodels theory.
Source arXiv, 1609.0274
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