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Effect Algebras with the Riesz Decomposition Property and AF C*-Algebras

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Abstract

Relations between effect algebras with Riesz decomposition properties and AF C*-algebras are studied. The well-known one-one correspondence between countable MV-algebras and unital AF C*-algebras whose Murray-von Neumann order is a lattice is extended to any unital AF C* algebras and some more general effect algebras having the Riesz decomposition property. One-one correspondence between tracial states on AF C*-algebras and states on the corresponding effect algebras is proved. In particular, pure (faithful) tracial states correspond to extremal (faithful) states on corresponding effect algebras.

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Pulmannova, S. Effect Algebras with the Riesz Decomposition Property and AF C*-Algebras. Foundations of Physics 29, 1389–1401 (1999). https://doi.org/10.1023/A:1018809209768

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