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Some More Functional Analysis

Posted: Wed Jul 13, 2016 6:22 pm
by Tsakanikas Nickos
Let \[ \displaystyle l_{1} = \left\{ x = ( \xi_{k} )_{k\in \mathbb{N}} \subset \mathbb{R} \; \Big| \; \sum_{k=1}^{\infty} | \xi_{k} | < \infty \right\} \]and let \[ \displaystyle c_{0} = \left\{ x = ( \xi_{k} )_{k\in \mathbb{N}} \subset \mathbb{R} \; \Big| \; \xi_{k} \rightarrow 0 \right\} \] Show that the dual space \( (c_{0})^{*} \) of \( c_{0} \) is isometrically isomorphic to \( l_{1} \).