show that $C([0, 1])$ is not a Banach space with the given norm
60685
The vector space formed on C[0,1] and the norm $(\int_{0}^{1}|f(t)|^2 dt)^{1/2} $
45432
Showing that $f:(0,2\pi]\to S^1$ is not a homeomorphism
81229
Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space
7345
Is $C[0,1]$ a Banach space for the $L^1$ norm?
51177
When are two norms equivalent on a Banach space?
65876
A normed space of continuous functions with norm $\int_{0}^{1}|f(t)|dt$ is not complete
150572
Explicit norm on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$
129087
Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
78654
An example of a norm which can't be generated by an inner product
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
132491
How to show that $C=C[0,1]$ is a Banach space
136538
How can I show that a bijection between $[0,1)$ and $(0,1)$ cannot be continuous?
155621
Finiteness of the dimension of a normed space and compactness
26183
Prob. 9, Sec. 4.3 in Kreyszig's Functional Analysis Book: Proof of the Hahn Banach Theorem without Zorn's Lemma
71848
Show that $(L^{p},\|\|_{p})$ is a Banach space.
157455
Show that the norm of the multiplication operator $M_f$ on $L^2[0,1]$ is $\|f\|_\infty$
80618
Surjective bounded operator in Banach spaces without bounded right-inverse