- #1

snoble

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Can someone give me a linear continuous map on [tex]l^\infty[/tex] that isn't the image of an element in [tex]l^1[/tex] by the canonical map [tex]\theta[/tex]

So that we are all using the same definitions here's what I use

[tex]l^1[/tex] is the space of complex sequences who's series absolutely converge

[tex]l^\infty[/tex] is the space of bounded complex sequences

[tex]C_0[/tex] is space of complex sequences that converges to 0

The canonical map [tex]\theta: X \rightarrow X^{**}[/tex] is defined as given [tex]x\in X[/tex] and [tex]x^*\in X^*[/tex] then [tex]\theta(x)(x^*) = x^*(x) [/tex]

So that there isn't any moral dilemmas I will just mention that this is not a homework assignment for a class. The only class that this could be related has already ended.

Thanks,

Steven