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Dual Space and Isometrically Isomorphic Spaces

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Let c be the set of all sequences *see attachment* , such that limit alpha_n exists.
Let be the dual space of c , and c consist of all functions f -> F, F or such that for every e>0 {n E : |f(n)| >E} is finite.
Show that c* is isometrically isomorphic to l'. Are c* and c isometrically isomorphic?

Please see the attachment for better symbol representation.

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Solution Summary

This solution investigates dual space and isometrically isomorphic spaces are investigated. It defines a natural map and uses the Hahn Banach theorem and determines if c* and c are isometrically isomorphic.

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