Details

Autor(en) / Beteiligte

• Bohata, Martin
• Hamhalter, Jan
• Kalenda, Ondřej F.K.

Titel

Decompositions of preduals of JBW and JBW⁎ algebras

Ist Teil von

• Journal of mathematical analysis and applications, 2017-02, Vol.446 (1), p.18-37

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2017

Link zum Volltext

Quelle

EZB-FREE-00999 freely available EZB journals

Beschreibungen/Notizen

• 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.