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May 14, 2018 at 2:30 comment added David Handelman Here is a ring proof. Let $R$ be a ring with $1$. If both $a,b$ are idempotents in $R$ st $1\pm (a-b)$ are invertible, then there is a simple argument to show that $a = xbx^{-1}$ for some invertible $x$ in $R$. In a C*-algebra ordinary equivalence implies *-equivalence, and you're done.
Oct 7, 2014 at 1:17 vote accept Martin Argerami
Dec 18, 2013 at 17:54 answer added Julien timeline score: 5
Dec 11, 2013 at 2:56 answer added Martin Argerami timeline score: 11
Dec 11, 2013 at 2:40 answer added Nik Weaver timeline score: 8
Dec 11, 2013 at 2:38 answer added voldemort timeline score: 2
Dec 11, 2013 at 2:23 answer added Qiaochu Yuan timeline score: 12
Dec 11, 2013 at 0:42 history asked Martin Argerami CC BY-SA 3.0