Some inverse limits of Cuntz algebras

Katsunori Kawamura

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arXiv · 1112.2769

Some inverse limits of Cuntz algebras

Katsunori Kawamura

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Abstract

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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Katsunori Kawamura. 2011-12-13. Some inverse limits of Cuntz algebras. https://arxiv.org/abs/1112.2769

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