C*-algebras whose every C*-subalgebra is AF

Details C*-algebras whose every C*-subalgebra is AF C*-algebras whose every C*-subalgebra is AF

2010-08-23

arxiv.org/abs/1008.3748v1

Mathematics

Operator Algebras

Scientific paper

Let $A$ be a $C^*$-algebra. It is shown that the following conditions are
equinvalent:
(1) $A$ is scattered,
(2) every $C^*$-subalgebra of $A$ is AF,
(3) every $C^*$-subalgebra of $A$ has real rank zero.

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