Uniformly hyperfinite algebra: Difference between revisions

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In [[mathematics]], particularly in the theory of [[C*-algebras]], a '''uniformly hyperfinite''', or '''UHF''', algebra is a C*-algebra that can be written as the closure, in the [[Operator norm|norm topology]], of an increasing union of finite -dimensional full [[matrix ring|matrix algebras]].

== Definition and classification ==

A UHF C*-algebra is the [[direct limit]] of an inductive system {''A_n'', ''φ_n''} where each ''A_n'' is a finite -dimensional full matrix algebra and each ''φ_n'' : ''A_n'' → ''A''_''n''+1 is a unital embedding. Suppressing the connecting maps, one can write

:<math>A = \overline {\cup_n A_n}.</math>