Dual norm

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The concept of a dual norm arises in functional analysis, a branch of mathematics.

Let X be a Banach space with norm ||.||. Then the dual space X* is the collection of all continuous linear functionals from X into the base field (which is either R or C). If L is such a linear functional, then the dual norm of L is defined by

\|L\|=\sup\{|L(x)|: x\in X, \|x\|\leq 1\}.

With this norm, the dual space is also a Banach space.

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