Definition 14.3.2 ($l^{\infty}$-Direct Product).label Let $\seqi{X}$ be normed vector spaces over $K \in \RC$ and $p \in [1, \infty)$, then the $l^{\infty}$-direct product of $\seqi{X}$ is the space
\[[l^{\infty}(I); X_{i}] = \bracs{x \in \prod_{i \in I}X_i \bigg | \sup_{i \in I}\norm{x_i}_{X_i} < \infty}\]
equipped with the norm
\[\norm{x}_{[l^\infty(I); X_i]}= \sup_{i \in I}\norm{x_i}_{X_i}\]
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