How to show that $\exists$ $\phi\in C_c^{\infty}(\Omega)$ s.t. $\int_{\Omega_1}D\phi(x)dx$ has unit norm?
91616
Existence of a $C_c^{\infty}$ function $\Phi$ s.t. $\int \nabla \Phi \neq 0.$
143869
Showing that the norm of the canonical projection $X\to X/M$ is $1$
144656
Linear functional and a bounded norm
56429
Extension of partial derivatives and the definition of $C^k(\overline{\Omega})$
113970
Compute $\int_cd\omega$ and $\int_{\partial c}\omega$
6270
Poincaré inequality for a subspace of $H^1(\Omega)$
59697
Is the boundary of the unit sphere in every normed vector space compact?
60685
The vector space formed on C[0,1] and the norm $(\int_{0}^{1}|f(t)|^2 dt)^{1/2} $
63124
Show that $ \lVert A \rVert_2^2 \leq \lVert A \rVert _1 \lVert A \rVert _ \infty $
76689
How to prove $C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$?
9159
$L^p$-norm of a non-negative measurable function
21881
Prove that $\forall\alpha\geq\omega$, $|L_\alpha|=|\alpha|$ without AC
34173
Banach spaces and their unit sphere
93511
Prove that $C^1([a,b])$ with the $C^1$- norm is a Banach Space
156727
A step in the proof of Characterization of $W^{1,\infty}$
92588
Showing that $(C_0([0,\infty)), \|\cdot\|_\infty)$ is complete.
71350
Let $H$ be a Hilbert space with projections $P,Q$, then $\lim_{n\to\infty}(PQ)^nx= Rx$ for all $x\in H$, where $R$ is the projection to $PH\cap QH$