https://math.codidact.com/categories/41/tags/6409.rssNew Posts Tagged 'normed-vector-space' - MathematicsMathematics - Codidact2022-01-31T16:28:15Zhttps://math.codidact.com/posts/285756$\{f_n\}\to f$ in $X$ implies $||f||\le\liminf||f_n||$ whybecauseâ€https://math.codidact.com/users/550222022-01-31T02:27:52Z2022-01-31T16:28:15Z<p>Let $X$ be a normed linear space and suppose that, for each $f\in X$ there exists a bounded linear functional $ T\in X^* $ such that $T(f)=||f||$ and $||T||_*=1$. Prove that if $\{f_n\}\to f$ in...