Application of Hahn–Banach theorem
100161
Is it true that $\dim(X) \leq \dim(X^{\ast})$ for every infinite dimentional Banach space $X$?
82355
When is the image of a linear operator (between Banach spaces) closed?
111475
Uniform convergence and the supremum theorem
28731
Banach space in functional analysis
132869
Show that any bounded linear functional on a normed linear space is continuous
71848
Show that $(L^{p},\|\|_{p})$ is a Banach space.
17159
Proof of Closest Point Theorem in Hilbert Space
93511
Prove that $C^1([a,b])$ with the $C^1$- norm is a Banach Space
47693
Applying Arzela-Ascoli to show pointwise convergence on $\mathbb{R}$.
100282
Measure Convergence Version of Lebesgue Dominated Convergence Theorem
57609
Hahn-Banach proof by extension of basis
151046
Closure of the invertible operators on a Banach space
139272
On the norm of a quotient of a Banach space.
155974
Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
156161
Banach-Tarski theorem without axiom of choice
64840
A Banach space that is not a Hilbert space
11558
How to show that the limit of compact operators in the operator norm topology is compact