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Triangular UHF algebras
Journal article   Open access   Peer reviewed

Triangular UHF algebras

Richard L Baker
Journal of functional analysis, Vol.91(1), pp.182-212
1990
DOI: 10.1016/0022-1236(90)90052-M
url
https://doi.org/10.1016/0022-1236(90)90052-MView
Published (Version of record) Open Access

Abstract

In this paper we classify triangular UHF algebras. The generic triangular UHF algebra is constructed as follows. Let ( p n ) be any sequence of positive integers such that p m | p n whenever m ⩽ n . For each n let T p n be the algebra of all p n × p n upper triangular complex matrices, and for m ⩽ n , let σ p n · p m : T p m → T p n be the mapping, x ↦1 d ⊗ x , where d = p n p m . A triangular UHF algebra (TUHF) of rank (p n ) is any Banach algebra that is isometrically isomorphic to the Banach algebra inductive limit T = lim n → ∞ ( T p n ; σ P m ). The principal result of the paper is that if J and T are arbitrary TUHF algebras, then J is isometrically isomorphic to T if, and only if J and T have the same supernatural number.

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