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Given a Banach space $X$. Consider the space $\ell_\infty(X)$ which is the $\ell_\infty$-sum of countably many copies of $X$. Is there any accessible respresentation of the dual space $\ell_\infty(X)^*$? In particular, is this dual space isomorphic to the space of finitely additive $X^*$-valued measures on the powerset of $\mathbb N$ equipped with the semivariation norm?

Any references will be appreciated.

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    Is $E = X$ in your question?2012-11-18
  • 0
    Oh yes, sorry. I'll correct it.2012-11-18

1 Answers 1