9 problems

For $1\leqslant p\leqslant2$, let $\operatorname{SEP}^n(L_p)$ be the supremum of the separation modulus over subsets of $L_p$ of cardinality at most $n$, where the separation modul…

Let $X$ be a separable Fraïssé Banach space, with the finite-dimensional approximate extension property defining Fraïssé spaces. The Fraïssé-space classification conjecture. Every…

A Fraïssé Banach space is a Banach space satisfying the finite-dimensional approximate extension property described by approximation of every sufficiently good finite-dimensional e…

A Banach space $X$ is Fraïssé when for every $\varepsilon>0$ and every $k\in\mathbb{N}$ there is a $\delta>0$ such that for every $k$-dimensional subspace $E$ of $X$ and every…

Let $X$ be a separable reflexive Fraïssé Banach space, where Fraïssé means that for every $\varepsilon>0$ and every $k\in\mathbb{N}$ there is $\delta>0$ such that every $k$-dimensi…

Let $X$ be a separable approximately ultrahomogeneous Banach space, meaning that the action of its linear isometry group has the corresponding finite-dimensional approximate transi…

Sharp-value conjecture. For all $p,q\in[1,\infty)$,

Let $\mathrm{H}$ be a collection of bandwidths, and let $\psi_\varepsilon$ be the upper function from the preceding deviation theorem. In the isotropic constant-bandwidth case, the…

Let $X$ be a subspace of some $L_p$ space, where $2<p<\infty$, and suppose that $\ell_p(\aleph_1)$ does not embed into $X$. Finite-measure embedding conjecture. Then $X$ embeds int…