Does it necessarily follow that $C^{n, \gamma}(\overline{X})$ is a Banach space?
134492
Proving that a Hölder space is a Banach space
154625
$\operatorname{span}(x^0, x^1, x^2,\cdots)$ and the vector space of all real valued continuous functions on $\Bbb R$
97621
Every separable Banach space is isomorphic to $\ell_1/A$ for some closed $A\subset \ell_1$
26183
Prob. 9, Sec. 4.3 in Kreyszig's Functional Analysis Book: Proof of the Hahn Banach Theorem without Zorn's Lemma
140379
Cauchy sequence in a discrete space
156855
separable Banach space with Banach-Mazur distances to $\ell_2^n$ bounded must be isomorphic to $\ell_2$?
14516
The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
18877
$f(z)$ and $\overline{f(\overline{z})}$ simultaneously holomorphic
57055
Are $|X|$ and $\operatorname{sgn}(X)$ independent?
82464
$U^*\otimes V$ versus $L(U,V)$ for infinite dimensional spaces
126744
Is any Banach space a dual space?
97949
Existence of a $\mathbb C$-Banach space isometric to a Hilbert Space but whose norm is not induced by an inner product?
63608
Cauchy sequence in a normed space
104607
Hahn-Banach theorem, dual space
19294
‎If ‎‎$‎X$ is an infinite-dimensional Banach space and ‎‎$‎‎u‎\in ‎B(X)‎$ ,then $\bigcap_{v\in K(X)}\sigma(u+v) =\cdots$
43826
Example to prove that $ C^1[0,1] $ is not a Banach space for the uniform norm?
109632
Show reflexive normed vector space is a Banach space