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'Minimal ideal'? I can understand why the quotient by a maximal ideal might be simple. Charles Matthews 19:34, 29 August 2006 (UTC)
- should be maximal to justify the simplicity claim, i think. it's actually the unique norm-closed ideal. Mct mht 14:55, 8 September 2007 (UTC)
What is the role separability plays? My guess is it is needed for the maximality of the ideal. Now that I think about it on a huge space the operators with separable range might form an ideal bigger than the compacts. Scineram (talk) 12:15, 11 December 2009 (UTC)