It is shown that the algebraic dimension of an infinite dimensional Banach space is equal to it's cardinality. Using this fact, can we say that the algebraic dimension of $(\ell^{\infty}(X))^*$is equal to $2^{2^X}$. Here $X$ is an arbitrary set.
2026-04-03 11:59:30.1775217570
Algebraic dimension of the dual of $\ell^{\infty}$
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