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- #1

- Jan 26, 2012

- 995

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**Background Info**: Let $X$ be a normed linear space. The linear operator $J:X\rightarrow X^{\ast\ast}$ defined by

\[J(x)[\psi] = \psi(x) \text{ for all $x\in X$, $\psi\in X^{\ast}$}\]

is called the

*natural embedding*of $X$ into $X^{\ast\ast}$.

**Problem**: Let $X$ be a normed linear space. Show that the natural embedding $J:X\rightarrow X^{\ast\ast}$ is an isometry.

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