All Questions

In "The Banach-Mazur distance to the cube and the Dvoretzky-Rogers factorization" Szarek and Bourgain prove a proportional Dvoretzky-Rogers factorization : Given $1>\delta>0$ , there ...

Let $K$ be a compact metric space; $\Delta K$ be the set of Borel probability measures on $K$ endowed with the weak* topology; $X$ be a closed subset of $\Delta K$; and $x_0 \in \overline{\text{co}} X$...

Let $X$ be a Banach space and let $A$ be a closed, convex and balanced subset of $B_{X^{*}}$ (where $B_{X^{*}}$ denotes the closed unit ball of the dual $X^{*}$). Is there a closed subspace $M$ of $X$ ...

Let $K$ be a bounded closed convex subset of a Banach space $E$. A point $x$ in $K$ is called a diametral point if $$ \sup_{y\in K} \|x-y\|={\rm diam}(K). $$ where ${\rm diam}(K)$ denotes the ...

I am considering the $L^1$ ball in $\mathbb{R}^d$, and a conservative vector field $V$ on it, which arises as the gradient of a bounded, almost-everywhere Lipchitz-function. Denoting by $e_i$ as the i’...