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Kadison’s antilattice theorem for a synaptic algebra

Foulis D. J., Pulmannová S.

Demonstratio Mathematica

2018

Vol. 51, nr 1

1--7

We prove that if A is a synaptic algebra and the orthomodular lattice P of projections in A is complete, then A is a factor if and only if A is an antilattice. We also generalize several other results of R. Kadison pertaining to infima and suprema in operator algebras.

On limit theorems in JW-algebras

Karimov A., Mukhamedov F.

Probability and Mathematical Statistics

2010

Vol. 30, Fasc. 1

153--165

In the present paper, we study bundle convergence in JW- algebra and prove certain ergodic theorems with respect to such convergence. Moreover, conditional expectations of reversible JW-algebras are considered. Using such expectations, the convergence of supermartingales is established.