Prove $C[a,b]$ with norm $\Vert f\Vert=\left(\int\limits_{a}^b\vert f(t)\vert^2\right)^{\frac{1}{2}}$ is not Banach space
93606
Showing that $C[0,1]$ is not complete
125277
Image of the tensor product of strict maps of Banach spaces
150287
Spectral radii and norms of similar elements in a C*-algebra: $\|bab^{-1}\|<1$ if $b=(\sum_{n=0}^\infty (a^*)^n a^n)^{1/2}$
60685
The vector space formed on C[0,1] and the norm $(\int_{0}^{1}|f(t)|^2 dt)^{1/2} $
61799
Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$
71848
Show that $(L^{p},\|\|_{p})$ is a Banach space.
123505
how to prove vector norm equivalence in finite dimensional space($\mathbb{R}^{n}$)?
115350
An example of a Banach space isomorphic but not isometric to a dual Banach space
127121
The identity cannot be a commutator in a Banach algebra?
82355
When is the image of a linear operator (between Banach spaces) closed?
96717
Hahn-Banach Theorem for separable spaces without Zorn's Lemma
124458
Quotient of a Banach space $X$ gets quotient topology under standard norm induced from $X$.
96363
How to show that $\mathbb R^n$ with the $1$-norm is not isometric to $\mathbb R^n$ with the infinity norm for $n>2$?
76689
How to prove $C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$?
63193
Proof that $\vert\int_a^bf(t)dt\vert\le\int_a^b\vert f(t)\vert dt $ for complex integration
9957
Prove if $f:[a,b] \rightarrow \mathbb{R}$ is integrable, then so is $|f|$ and $\left|\int_{a}^{b}f(x)dx\right| \leq \int_{a}^{b}|f(x)|dx$
66084
Prove 1-Norm is a Norm