Publikace na Matematicko-fyzikální fakulta |
2017
Abstrakt
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.