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Article overview
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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 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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