Banach space it isn't Hilbert space
64840
A Banach space that is not a Hilbert space
134575
Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
71848
Show that $(L^{p},\|\|_{p})$ is a Banach space.
76572
What facts about the weak topology fail in spaces that aren't Banach?
144112
Show that $c_0$ is a Banach space with the norm $\rVert \cdot \lVert_\infty$
125776
If space of bounded operators L(V,W) is Banach, V nonzero, then W is Banach (note direction of implication)
62428
How to prove this inequality in Banach space?
104607
Hahn-Banach theorem, dual space
73619
Why is $(\mathbb{R}, \mathcal{P}(\mathbb{R}))$ called a measurable space when actually is not?
64375
Non-Metrizable Topological Spaces
82355
When is the image of a linear operator (between Banach spaces) closed?
145952
Example of a closed subspace of a Banach space which is not complemented?
57609
Hahn-Banach proof by extension of basis
47231
The space $C^0([0;1],\mathbb{R})$ of all continuous, real-valued functions on $[0,1]$ is not reflexive.
146707
Formally show that the set of continuous functions is not measurable
83907
$f$ bounded but $f'$ isn't
71001
Do continuous linear functions between Banach spaces extend?