Proving that a convex subset of a Banach space can be totally bounded
114139
Convex Hull of Precompact Subset is Precompact
31548
Proof of "every convex function is continuous"
35857
Characterization of log-convexity
38896
Prove that $A$ is bounded operator on $\ell^p$ and find $\| A\|$
71848
Show that $(L^{p},\|\|_{p})$ is a Banach space.
19294
‎If ‎‎$‎X$ is an infinite-dimensional Banach space and ‎‎$‎‎u‎\in ‎B(X)‎$ ,then $\bigcap_{v\in K(X)}\sigma(u+v) =\cdots$
115495
Prove $\int _0^\infty f^2 dx \leq \cdots $ for $f$ convex
158399
Show that $\{(x_1,x_2):x_1x_2\geq4,x_1>0,x_2>0\}$ is a convex set
7345
Is $C[0,1]$ a Banach space for the $L^1$ norm?
156855
separable Banach space with Banach-Mazur distances to $\ell_2^n$ bounded must be isomorphic to $\ell_2$?
71619
Proving that a convex function is Lipschitz
132869
Show that any bounded linear functional on a normed linear space is continuous
120648
Proof Check: Every Cauchy Sequence is Bounded
20120
Converging series in Banach space
140813
How do i prove that continuous linear transformation between normed spaces is bounded?
144372
How to Prove that if $A$ is bounded, then $A \cdot A$ is bounded?
30572
Intersection of nested closed bounded convex sets in Euclidean space