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Can anyone give me an example of an operator $T:\ell^\infty\rightarrow\ell^\infty$ which has dense range but is not surjective?

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I assume you require $T$ to be continuous and linear? –  Alex Becker Jul 7 '12 at 22:29
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The same question was asked on MO and deemed nontrivial by Bill Johnson mathoverflow.net/questions/101253 –  user35340 Jul 7 '12 at 23:06
    
Seems that the OP was the one to ask it on MO as well. –  Asaf Karagila Jul 7 '12 at 23:09
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This was originally posted on MO: mathoverflow.net/questions/101253/… –  user16299 Jul 7 '12 at 23:20
    
@ellinfinity: Because you do not have 50 reputation points yet, you can only comment on your own questions and answers. So, the "add comment" button will only appear for you once you gain 50 points. –  Zev Chonoles Jul 7 '12 at 23:42
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