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A NONSEPARABLE AMENABLE OPERATOR ALGEBRA WHICH IS NOT ISOMORPHIC TO A $C^*$ -ALGEBRA

  • YEMON CHOI (a1), ILIJAS FARAH (a2) (a3) and NARUTAKA OZAWA (a4)

Abstract

It has been a long-standing question whether every amenable operator algebra is isomorphic to a (necessarily nuclear) $\mathrm{C}^*$ -algebra. In this note, we give a nonseparable counterexample. Finding out whether a separable counterexample exists remains an open problem. We also initiate a general study of unitarizability of representations of amenable groups in $\mathrm{C}^*$ -algebras and show that our method cannot produce a separable counterexample.

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References

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A NONSEPARABLE AMENABLE OPERATOR ALGEBRA WHICH IS NOT ISOMORPHIC TO A $C^*$ -ALGEBRA

  • YEMON CHOI (a1), ILIJAS FARAH (a2) (a3) and NARUTAKA OZAWA (a4)

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