Can anyone give me an example of an operator $T:\ell^\infty\rightarrow\ell^\infty$ which has dense range but is not surjective?
surjectivity of operators on $\ell^\infty$
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functional-analysis
operator-theory
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0I assume you require $T$ to be continuous and linear? – 2012-07-07
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1This was originally posted on MO: http://mathoverflow.net/questions/101253/surjectivity-of-operators-on-linfty – 2012-07-07
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2The same question was asked on MO and deemed nontrivial by Bill Johnson http://mathoverflow.net/questions/101253/ – 2012-07-07
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0Seems that the OP was the one to ask it on MO as well. – 2012-07-07
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0@ellinfinity: Because you do not have 50 reputation points yet, [you can only comment on your own questions and answers](http://meta.stackexchange.com/questions/19756/how-do-comments-work/19757#19757). So, the "add comment" button will only appear for you once you gain 50 points. – 2012-07-07
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0@ZevChonoles I don't understand; how has ellinfinity's comment appeared, then? – 2012-07-08
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0@YemonChoi: Mods have the power to turn answers into comments. – 2012-07-08