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arXiv · 1511.01086

Decompositions of preduals of JBW and JBW$^*$ algebras

Martin Bohata·Jan Hamhalter·Ondřej F. K. Kalenda
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Abstract

We prove that the predual of any JBW$^*$-algebra is a complex $1$-Plichko space and the predual of any JBW-algebra is a real $1$-Plichko space. I.e., any such space has a countably $1$-norming Markushevich basis, or, equivalently, a commutative $1$-projectional skeleton. This extends recent results of the authors who proved the same for preduals of von Neumann algebras and their self-adjoint parts. However, the more general setting of Jordan algebras turned to be much more complicated. We use in the proof a set-theoretical method of elementary submodels. As a byproduct we obtain a result on amalgamation of projectional skeletons.

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Martin Bohata, Jan Hamhalter, Ondřej F. K. Kalenda. 2016-09-02. Decompositions of preduals of JBW and JBW$^*$ algebras. https://doi.org/10.1016/j.jmaa.2016.08.031

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