7 problems

Krivine's conjecture. The bound obtained from Krivine's original scheme is exactly the value of the Grothendieck constant $K_G$.

Let $\mathcal{E}=(E_n)_{n\geqslant 1}$ be a sequence of finite-dimensional Banach spaces with $\dim E_n=n$, and let $F$ be a Banach space with the bounded approximation property. A…

Let $d,m,n\in\mathbb{N}$. The real symmetric spaces $\mathbb{S}^n(\mathbb{R})$, real rectangular spaces $\mathbb{R}^{m\times n}$, complex symmetric spaces…

Let $d$ be a positive integer and let $T=(T_{ijkl})_{i,j,k,l=1}^d$ be a four-dimensional array of complex numbers. Define … where the supremum is over pairs of $d\times d$ unitary…

Let $f_\eta:\mathbb R^2\to\{-1,1\}$ be the family of measurable functions defined in the paper, and let $c(f,g)$ denote the associated Krivine rounding constant. The planar roundin…

For a measure-space formulation of Grothendieck's inequality, let $K:\mathbb R^n\times\mathbb R^n\to\mathbb R$ be the oscillatory Gaussian kernel … and let … Define…

Haagerup's conjecture. The complex Grothendieck constant satisfies