Some inverse limits of Cuntz algebras

Details Some inverse limits of Cuntz algebras Some inverse limits of Cuntz algebras

2011-12-13

arxiv.org/abs/1112.2769v1

Mathematics

Operator Algebras

24 pages

Scientific paper

We construct a nontrivial inverse system of Cuntz algebras $\{{\cal
O}_{n}:2\leq n<\infty\}$, whose inverse limit is *-isomorphic onto ${\cal
O}_{\infty}$. By using this result, it is shown that the $K_{0}$-functor is
discontinuous with respect to the inverse limit even if the limit is a
C$^{*}$-algebra.

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