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Does, there exist a Banach algebra with a family of right units with norms converging to 1, but without right unit of norm 1?

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  • $\begingroup$ @YemonChoi, $C_0(X)$ is commutative, so right units are just units. But $C_0(X)$ with $X$ non-compact is not unital. So how does $C_0(X)$ answer my question? $\endgroup$
    – Norbert
    Commented Jul 24, 2014 at 10:21
  • $\begingroup$ my mistake, I misread your question as asking about right approximate units. I've deleted my previous comment. Sorry. $\endgroup$
    – Yemon Choi
    Commented Jul 24, 2014 at 17:22
  • $\begingroup$ @YemonChoi, no problem. Just do me a favour, do not put this question on hold. $\endgroup$
    – Norbert
    Commented Jul 24, 2014 at 21:31

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