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Convergences in JW-algebras and in their enveloping von Neumann algebras

Abstract

We study properties of different convergences in JW-algebras with a faithful normal state. The relationship between these convergences and similar convergences in enveloping von Neumann algebras is established. Based on this, ergodic theorems are proved.

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Correspondence to A. K. Karimov.

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Original Russian Text © A. K. Karimov, 2008, published in Matematicheskie Trudy, 2008, Vol. 11, No. 1, pp. 68–80.

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Karimov, A.K. Convergences in JW-algebras and in their enveloping von Neumann algebras. Sib. Adv. Math. 18, 176 (2008). https://doi.org/10.3103/S1055134408030036

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Key words

  • convergence
  • enveloping algebra
  • ergodic theorem