10 problems

Let $\mathbb{X}$ be a Banach space with a unique unconditional basis. For $E\in\{c_{0},\ell_{1},\ell_{2}\}$, consider the iterated copy $E(\mathbb{X})$ of $\mathbb{X}$, namely the…

Let $0<p<\infty$ and let $\mathbb{X}$ be a quasi-Banach space. Suppose that a vector-valued $L_p(\mathbb{X})$ space admits an averaging projection onto $\mathbb{X}$. Kalton's conje…

Countable-chain-condition conjecture. For every $p$-natural quasi-Banach space $E$, the space

The non-resonant boundedness conjecture. Up to end-points, both operators have the boundedness range

Let $X$ be an $r$-convex and $s$-concave quasi-Banach function space over $\mega$ and suppose that $\mathcal{E}$ has the $A_1$ self-improvement property. Suppose that … is bounded.…

Let $S_p^N$ and $S_q^N$ be Schatten classes of $N\times N$ matrices, and let $d_n$ denote the $n$th Kolmogorov number of the embedding. For $0<p\leq\infty$, $0<q\leq1$, $q\leq p$,…

The paper considers normed interpolation spaces between $\ell^{1}$ and $\ell^{q}$, and Theorem 4.1 establishes the relevant characterization for positive exponents in the normed se…

Let $0<p<1$, let $\mathcal{M}=(M_k)_{k\geq 0}$ be the weight sequence defining the quasi-norm … and let $\widehat{\mathcal{S}}$ be the completion of the subclass $\mathcal{S}$ with…

Let $0<p<1$, let $\mathcal{M}=(M_k)_{k\geq 0}$ be the weight sequence defining the quasi-norm … and let $\widehat{\mathcal{C}}$ be the completion of $C^{\infty}$ with respect to th…

Democracy characterization conjecture. If