Infinite order decompositions of C$^*$-algebras
F.N. Arzikulov

TL;DR
This paper investigates infinite order decompositions of C*-algebras, providing proofs that connect monotone completeness and ultraweak closure to the structure of von Neumann algebras.
Contribution
It establishes conditions under which infinite order decompositions of C*-algebras are themselves C*-algebras or von Neumann algebras, clarifying their structural relationships.
Findings
Monotone complete order unit spaces are C*-algebras.
Monotone complete C*-algebras are von Neumann algebras.
Certain C*-algebra decompositions are von Neumann algebras.
Abstract
In the given article infinite order decompositions of C-algebras are investigated. We give complete proofs of the following statements: 1) If the order unit space is monotone complete in (i.e. ultraweakly closed), then is a C-algebra. 2) If is monotone complete in (i.e. a von Neumann algebra), then . 3) If is a C-algebra then this algebra is a von Neumann algebra.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Holomorphic and Operator Theory
