9 problems

Interpolation conjecture. The quasi-Banach spaces defined in the paper are complex interpolation spaces, completely isometrically, in the sense that

Let $d$ be a positive integer, let $m_\delta$ be the Bochner–Riesz multiplier from the classical formulation, and let $\mathfrak{M}_p({\mathbb R}^{2d})$ denote the class of multipl…

Let $p:\{-1,1\}^n\to\mathbb{R}$ be a polynomial of degree at most $d$. Its Fourier completely bounded $d$-norm is denoted by $\|p\|_{\operatorname{fcb},d}$, and…

Let $X$ be a valid norm, meaning a norm on $\mathcal{S}_1^{\tilde k'\!, n}\otimes\mathcal{S}_1^{\tilde k'\!, n}\otimes\ell_2^{k\tilde k'}$ satisfying … for every $x$, together with…

Let $X$ be a norm on the algebraic tensor product $\mathcal{S}_1^{\tilde k'\!, n}\otimes\mathcal{S}_1^{\tilde k'\!, n}\otimes\ell_2^{k\tilde k'}$. Call $X$ valid if … for every $x$…

Weaker-form conjecture. There exists a dimension-independent constant $\beta<1$ such that

Let $n$, $k$, and $\tilde k'$ be the parameters in the construction, let $\mathcal{S}_1^{\tilde k'\!, n}$ denote the corresponding trace-class space, let…

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…

Let $G$ be a locally compact group and let ${\mathrm{A}(G)}$ denote its Fourier algebra. Operator biflatness conjecture. ${\mathrm{A}(G)}$ is always operator biflat. This would ext…