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Nov 23, 2018 at 11:24 history edited Martin Sleziak
the tag (oa.operator-algebras) also seems suitable here
Nov 16, 2018 at 16:10 vote accept Darman
Nov 16, 2018 at 15:39 answer added Nik Weaver timeline score: 8
Nov 16, 2018 at 15:20 history edited Darman CC BY-SA 4.0
added 2 characters in body; edited tags
Nov 16, 2018 at 14:41 history undeleted Darman
Nov 16, 2018 at 13:20 history deleted Darman via Vote
Nov 16, 2018 at 12:26 comment added Yemon Choi Small observation: every $C^*$-subalgebra of $J$ is contained in $J \cap J^*$, so your question is equivalent to asking if $J\cap J^*$ is infinite-dimensional for every infinite-dimensional closed right ideal $J\subset A$.
Nov 16, 2018 at 9:34 history asked Darman CC BY-SA 4.0