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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: About the proof that L1 is the dual of c0
Replies: 9   Last Post: Nov 6, 2006 9:08 PM

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Lynn Kurtz

Posts: 1,278
Registered: 12/6/04
Re: About the proof that L1 is the dual of c0
Posted: Oct 21, 2006 5:25 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 21 Oct 2006 08:16:28 -0700, "nkorppi" <korpelainen@gmail.com>
wrote:

>On page 104 of these Functional Analysis notes
>(http://www.mth.kcl.ac.uk/~iwilde/notes/fa2/fa2.pdf) , the author gives
>a proof that L1 is the dual of c0.
>
>On the next page he explains the general argument, due to Hahn-Banach,
>which shows that L1 is not the dual of L{infinity}.
>
>However, in the proof itself, I cannot really see how the fact that
>sequences converge to zero is used? How would the 'onto' -part of the
>proof go wrong if c0 were to be replaced by L{infinity}?
>
>I'm going beserks trying to figure it out...

And of course you have the author's permission to post these notes for
all the world to copy.

--Lynn

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