12 problems

Let … of $^n$, and let $1<pbackslashle 2$. Let $A^p$ denote the Bergman space, let $T$ be the Toeplitz operator induced by … be its Berezin transform, and let $K(,)$ be the Bergma…

Absolute summability conjecture for exact interpolation spaces. The embedding

Endpoint absolute summability conjecture. The inclusion

Let $X$ and $Y$ be real Banach spaces. The pair $(X,Y)$ has the Hilbert space factorization property (HFP) when every bounded operator $\phi:X\to Y$ satisfies…

Let $1<p<2$, set $r=2p/(2-p)$, and let $i_{p2}\colon\ell_p\to\ell_2$ be the formal identity map. Let $\pi_{r,2}(\cdot)$ denote the $(r,2)$-absolutely summing norm. For a linear map…

GKS's conjecture. The approximation numbers satisfy

Let $G$ be a compact abelian group, let $Z(G)$ be an invariant function space, and let $T:H_1\to H_2$ be an operator between Hilbert spaces. Say that $T$ factorizes invariantly thr…

Let $W^{1}_{1}$ denote the Sobolev space on the relevant torus, and let $T$ be an operator between Hilbert spaces that factorizes through $W^{1}_{1}$. Invariant little Grothendieck…

Soient $E$ et $F$ deux espaces de Banach. Un opérateur pré-Hilbert-Schmidt est un opérateur $u:E\to F$ de cette classe; un espace de Hilbert-Schmidt est l'espace à travers lequel u…

Let $d_{w,p}$ be the Lorentz sequence space. Let $\mathcal{SS}$ denote the ideal of strictly singular operators on $d_{w,p}$, let $J^j$ be the ideal generated by the formal identit…

Let $d_{w,p}$ be the Lorentz sequence space, and let $cmathcal K(d_{w,p})$ denote the ideal of compact operators on it. Let $j\colon\ell_p\to d_{w,p}$ be the formal identity, and w…

Let $\mathcal{X}$ be a Banach space such that … where $1\leq p\leq\infty$ or $p=0$ (we say that such a space admits a Pełczyński decomposition). Assume that…