Prove that operator between Banach spaces is continuous
135661
Weakly continuous operators are continuous
82355
When is the image of a linear operator (between Banach spaces) closed?
2439
If a linear operator has an adjoint operator, it is bounded
84961
weak sequential continuity of linear operators
87239
Prove functions defined by sup and inf are continuous
31548
Proof of "every convex function is continuous"
111907
Prove that Cantor function is Hölder continuous
52922
let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
97158
Prove that the operator norm is a norm
110112
Proving a function is Lipschitz continuous
83054
Let $E$ be a Banach space, prove that the sum of two closed subspaces is closed if one is finite dimensional
62428
How to prove this inequality in Banach space?
57180
Techniques to prove a function is uniformly continuous
28731
Banach space in functional analysis
30210
A compact operator is completely continuous.
19294
‎If ‎‎$‎X$ is an infinite-dimensional Banach space and ‎‎$‎‎u‎\in ‎B(X)‎$ ,then $\bigcap_{v\in K(X)}\sigma(u+v) =\cdots$
117502
Proving that a certain continuous function is surjective.