Abstract:
A survey is given of the basic results of the theory of AW∗-algebras, the properties of the rings of measurable and locally measurable operators associated with von Neumann algebras and AW∗-algebras are described, Baer *-algebras admitting partial orderings compatible with their algebraic structures are investigated.
This publication is cited in the following 9 articles:
V. I. Chilin, Zh. A. Karimov, “Tsiklicheskaya kompaktnost v banakhovykh C∞(Q)-modulyakh”, Sovremennye problemy matematiki i fiziki, SMFN, 65, no. 1, Rossiiskii universitet druzhby narodov, M., 2019, 137–155
Sh. A. Ayupov, F. N. Arzikulov, “Reversible AJW-algebras”, Vladikavk. matem. zhurn., 18:3 (2016), 15–21
V. I. Chilin, Zh. A. Karimov, “Diz'yunktno polnye C∞(Q)-moduli”, Vladikavk. matem. zhurn., 16:2 (2014), 69–78
G. B. Levitina, V. I. Chilin, “Derivations on ideals in commutative AW∗-algebras”, Siberian Adv. Math., 24:1 (2014), 26–42
B. S. Zakirov, “Gomomorfizmy ∗-algebr lokalno izmerimykh operatorov”, Vladikavk. matem. zhurn., 12:2 (2010), 15–23
S. A. Albeverio, Sh. A. Ayupov, A. Kh. Abduvaitov, “On the coincidence of types of a real AW∗-algebra and its complexification”, Izv. Math., 68:5 (2004), 851–860
F. A. Sukochev, V. I. Chilin, A. F. Ber, “Derivations in Commutative Regular Algebras”, Math. Notes, 75:3 (2004), 418–419
I. G. Ganiev, V. I. Chilin, “Measurable Bundles of Noncommutative Lp-Spaces Associated with a Center-valued Trace”, Siberian Adv. Math., 12:4 (2002), 19–33
B. S. Zakirov, V. I. Chilin, “Abstract characterization of EW∗-algebras”, Funct. Anal. Appl., 25:1 (1991), 63–64