6 problems

Extended stability conjecture. For every cardinal $\alpha$, the intersection of every extendedly stable property with the set of Banach spaces with density character less than…

Montgomery-Smith–Semenov hypothesis. There exist signs $\theta_i\in\{-1,1\}$ and a constant $c_0>0$ such that

A complemented subspace of $L_1[0,1]$ is the range of a bounded projection on $L_1[0,1]$. Conjecture on complemented subspaces of $L_1[0,1]$. Up to isomorphism, the only complement…

Let $e_{\|.\|}$ be the largest number of vertices in an equilateral set in the normed space $(\mathbb{R}^d,\|.\|)$, and let $\ell_1^d$ denote $\mathbb{R}^d$ equipped with the…

Let $Y$ be an infinite-dimensional closed subspace of $L_1(0,1)$. An isomorphic copy of a Banach space $E$ in $Y$ means a subspace of $Y$ linearly isomorphic to $E$. Aldous's subsp…

Let $L_1$ denote the space of integrable functions, and let $K\subseteq L_1$ be compact and convex. Write $\mu_1^{L_1}(K)$ for the supremum of the first Holmes–Thompson intrinsic v…