Banach subspace of $C(X)$
138784
Is the differentiation operator an open mapping?
71848
Show that $(L^{p},\|\|_{p})$ is a Banach space.
26183
Prob. 9, Sec. 4.3 in Kreyszig's Functional Analysis Book: Proof of the Hahn Banach Theorem without Zorn's Lemma
116273
Does every $\mathbb{R},\mathbb{C}$ vector space have a norm?
91022
How do I prove that a subspace of a vector space $X$ is the null space of some linear functional on $X$?
151046
Closure of the invertible operators on a Banach space
33642
Finite dimensional subspace of $C([0,1])$
133777
Application of Banach-Steinhaus theorem
79061
show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
26989
Show that C[0,1] is a vector space
43826
Example to prove that $ C^1[0,1] $ is not a Banach space for the uniform norm?
137067
For Banach space there is a compact topological space so that the Banach space is isometrically isomorphic with a closed subspace of $C(X)$.
154625
$\operatorname{span}(x^0, x^1, x^2,\cdots)$ and the vector space of all real valued continuous functions on $\Bbb R$
81229
Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space
15839
equivalent norms in Banach spaces of infinite dimension
4151
Every subspace of a vector space has a complement
92497
Isometric Embedding of a separable Banach Space into $\ell^{\infty}$