10 problems

Let $S_p$ denote the Schatten $p$-class, and let $A,B,C\in S_p$. For $p>0$, write $\\|\cdot\\|_p$ for the Schatten $p$-quasi-norm. Sharp three-operator Clarkson–McCarthy conjecture…

Let $\mathscr{H}$ be a Hilbert space, let $\mathbb{B}_p(\mathscr{H})$ denote the Schatten $p$-class, and define $\omega_j=e^{ji\pi/n}$. Let…

Let $\mathscr{H}$ be a Hilbert space and let $\mathbb{B}_p(\mathscr{H})$ denote the Schatten $p$-class on $\mathscr{H}$. For $A,B\in\mathbb{B}_p(\mathscr{H})$, the noncommutative C…

Audenaert–Kittenah conjecture. For $1\le p\le 2$,

Audenaert–Kittaneh's conjecture. For $1<p\le 2$,

Two-dimensional Schatten embedding conjecture. For any $p\geq 1$ and $A,B\in\mathcal{S}_p$, the real space

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 Gelfand–approximation conjecture. One has

GKS's conjecture. The approximation numbers satisfy

Let $d4d8_p$ be the collection of symbols that are bounded Schur multipliers of the Schatten–von Neumann class $d4d4_p$, and let $d4d8_p^{\mathrm{cb}}$ be the collection of symbols…