Remarks on R

Details Remarks on R Remarks on R

2011-12-28

arxiv.org/abs/1112.6069v1

Mathematics

Operator Algebras

Scientific paper

The following results on the Jacelon C*-algebra R are obtained: (1) R is tensorially self-absorbing. (2) R-stability passes to sigma unital hereditary projectionless subalgebras. (3) If $A$ is a projectionless R-stable (or Z-stable) C*-algebra and $a,b\in A^+$, then $a$ is approximate unitarily equivalent to $b$ if and only if every lower semicontinuous 2-quasitrace induces the same measure on $C^*(a)$ and $C^*(b)$. (4) R may be characterized as an initial and as a terminal object in suitable categories of C*-algebras. Some evidence is given for the conjecture that amenable R-stable C*-algebras (simple and non-simple) are classified by their cones of traces.

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