10 problems

Bennett–Grosse-Erdmann conjecture. The displayed inequality, and respectively its reverse inequality, remain valid with the same best possible constant $(\alpha p+1)^p$ when…

Randrianantoanina's conjecture. The range of every contractive projection on $X$ admits a block basis.

Let $J$ be an index set, and give the product space … the product topology. Let $\mathbb{C}^{(J)}=\bigoplus_{j\in J}\mathbb{C}$ denote the space of finite sequences, equipped with…

Non-closure conjecture. The set of sequences preserving summability is not closed under addition.

Let $A = \operatorname{diag}(2^{a_1},\ldots,2^{a_d})$ and $B = \operatorname{diag}(2^{b_1},\ldots,2^{b_d})$ be diagonal matrices with anisotropies…

Let $V$ be a locally convex FK space, where $\ell_\infty$ denotes the space of bounded real sequences and $\{0,1\}^\omega$ is the space of binary sequences with its product topolog…

Albuquerque–Rezende's conjecture. There exist constants $B_{m},C_{m}>0$, depending only on $m$, such that

Non-ideality conjecture. The trace space $K^1_B\big|_{\{a_k\}}$ is never an ideal sequence space.

Optimal asymptotic estimate. There exist constants $B_d,C_d<\infty$ such that

Optimal-growth conjecture. The best possible condition on the growth of $\|x_n\|$ implying weak closeness of $\{x_n:n\in\mathbb N_0\}$ in $\ell_p$ is (kball) with $a=\min\{2,q\}$.