Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decompositions of preduals of JBW and JBW$^*$ algebras   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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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg