Decompositions of preduals of JBW and JBW^⁎ algebras

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• 作者：Martin Bohata^a ; ^{bohata@math.feld.cvut.cz" class="auth_mail" title="E-mail the corresponding author} ; Jan Hamhalter^a ; ^{hamhalte@math.feld.cvut.cz" class="auth_mail" title="E-mail the corresponding author} ; Ondřej F.K. Kalenda^b ; ^{kalenda@karlin.mff.cuni.cz" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Jordan algebra ; JBW-algebra ; Predual ; 1-Plichko space ; Weakly compactly generated space ; Projectional skeleton
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：18-37
• 全文大小：517 K

文摘

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.