Decompositions of preduals of JBW and JBW algebras

作者：Bohata Martin; Hamhalter Jan; Kalenda Ondrej F K^*

来源：Journal of Mathematical Analysis and Applications, 2017, 446(1): 18-37.

DOI：10.1016/j.jmaa.2016.08.031

• Jordan algebra
• JBW-algebra
• Predual
• 1-Plichko space
• Weakly compactly generated space
• Projectional skeleton

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.

• 出版日期2017-2-1