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Let $V$ be the Banach space of bounded sequences of reals with the sup norm. .Does there exists a subset $B$ of $V$ such that
If so, is an explicit such $B$ known? |
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Basis for L_infty(R)Let $V$ be the Banach space of bounded sequences of reals with the sup norm. . Does there exists a subset $B$ of $V$ such that Linear Independence: For all functions $c$ in $\mathbb{R}^B$, if $\displaystyle\sum_{b \in B} c(b) \cdot b \: = 0$, then $c$ is identically zero. Spanning Set: For all vectors $v$ in $V$, there exists a function $c$ in $\mathbb{R}^B$ such that $\displaystyle\sum_{b \in B} c(b) \cdot b \: = v$ . If so, is an explicit such $B$ known?
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