New posts in Functional Analysis

Is a bijective, norm-preserving and rotation-invariant mapping linear?

derivative of the $L^p$-norm with respect to $p$

Let $e,f$ be unit vectors in a real Banach space s.t $\|2e+f\|=\|e-2f\|=3$, show that $\|\lambda e+\mu f\|=|\lambda|+|\mu|$.

What is the motivation for sequences to be defined on natural numbers?

Bounded linear map which is not continuous

If $T:(\mathbb{R}^2,\|\cdot\|_p) \to (\mathbb{R}^2,\|\cdot\|_q)$ is an onto linear isometry, then must it be $p=q$?

How to prove a norm identity for a Banach space and its dual

$\frac{1}{2r}\int_{x-r}^{x+r}f(t)dt \to g(x)$ uniformly when $r\rightarrow \infty$, then $g(x)=ax+b$

Why is $f(t) = e^{ta}$ differentiable in a unital Banach algebra?

Let $X$ be a normed vector space. Let $T,S$ be bounded linear operators such that $T^2=T,S^2=S,ST=TS$. Show either $T=S$ or $\|T-S\|\geq 1$