A short proof of Elliott’s theorem:?_{2}⨂?_{2}≅?_{2}

C. R. Math. Rep. Acad. Sci. Canada Vol. 16 (1) 1994, pp. 31–36

(Received: 1994-03-07
)

M. Rørdam

**Abstract/Résumé:**

The purpose of this note is to present a direct and relatively self-contained proof of the theorem of George Elliott that 0 , ® O j is isomorphic to O2 This theorem will also be included in [2], where it will follow from a much more general result. The present proof differs from the proof given in [2], in that it gives a characterization of all separable unital C*-algebras A for which A is isomorphic to i4 ® O*. Most of the ideas of the proof given here are due to Elliott and are based on conversations, but there are some new ideas and short cuts, most notably in the proof of Lemma 1.

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A short proof of Elliott's theorem: ?2 ⨂ ?2 ≅ ?2