5 problems

Lorentz-space approximation and Gelfand number conjecture. Formula…

Let $1\le p\le\infty$ and let the semiaxes be $\sigma_j=j^{-\lambda}$ for $j\in\mathbb{N}$, with $\lambda>\frac{1}{s}=\left(\frac{1}{2}-\frac{1}{p}\right)_+$. Write…

The Gelfand–approximation conjecture. One has

For $0<p_0\leq 1$, $0<q_0\leq p_0\leq p_1\leq q_1\leq 2$ and $1/p_0-1/p_1<r<1/q_0-1/q_1$, let $c_m(\operatorname{Id}:S^r_{p_0,q_0}B([0,1]^d)\rightarrow S^0_{p_1,q_1}B([0,1]^d))$ de…

Let $1<p_1,p_2<2$ and … For the embedding ${\rm App}:S^t_{p_1,p_1}B(\Omega)\to L_{p_2}(\Omega)$, let $c_n({\rm App})$ denote its $n$-th Gelfand number. Sharpness conjecture. The up…