Possible Duplicate:
The Space $C(\Omega,\mathbb{R})$ has a Predual?
Is their Banach space such that its dual is C[a b] - continuos functions on [a b] ?
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Related question is:
The Space $C(\Omega,\mathbb{R})$ has a Predual?
It seems that comment by Jonas Meyer to this question contains a negative answer to my question. However some extension of comment is welcome - "by the Krein-Milman theorem this implies that is not a dual space." - not very clear to me.
PS Surprising how can similar questions come to mind of different people during the same day ?:)
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Background:
in finite-dimensions: double dual space is isomorphic to itself. In infinite-dimensions it is not always true. In particular for space of continuous functions it is not true (as far as I remember). (See Double dual of the space $C[0,1]$ ).
Remark: Dual space of continuous functions is quite well understood - it is a space of measures with bounded variation. See e.g. http://regularize.wordpress.com/2011/11/11/dual-spaces-of-continuous-functions/