Prove $ C^1[0,1]$ is not a Banach space with the sup-norm
97391
Prove that $(C^1[0,1], \|\cdot\|)$ is not a Banach space
93511
Prove that $C^1([a,b])$ with the $C^1$- norm is a Banach Space
97158
Prove that the operator norm is a norm
92497
Isometric Embedding of a separable Banach Space into $\ell^{\infty}$
14840
$c_0$ is a closed subspace of $l^{\infty}$
63453
A proof of the fact that the Fourier transform is not surjective from $\mathcal{L}^1(\mathbb{R})$ to $C_0( \mathbb{R})$
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
97621
Every separable Banach space is isomorphic to $\ell_1/A$ for some closed $A\subset \ell_1$
41620
The dual space of $c$ is $\ell^1$
118564
Dual cone of a $L^1$ norm cone?
64840
A Banach space that is not a Hilbert space
149997
Convolution operator has norm 1 with respect to $L^2$ norm
118903
The sup norm on $C[0,1]$ is not equivalent to another one, induced by some inner product
44738
Compact operators on an infinite dimensional Banach space cannot be surjective
43535
show that the interval of the form $[0,a)$ or $(a, 1]$ is open set in metric subspace $[0,1]$ but not open in $\mathbb R^1$
109632
Show reflexive normed vector space is a Banach space
33485
norm of integral operator in $C([0,1])$