9 problems

Hankel-product boundedness conjecture. The Hankel product $H_{\overline{f}}^{*}H_{\overline{g}}$ is bounded if and only if $D(f,g)$ is bounded.

Lunar-map SAP equivalence conjecture. The lunar condition on a map is equivalent to the SAP of its associated Hankel system.

Lunar–SAP equivalence conjecture. The local algebraic lunar condition on $\mathcal{M}$ is equivalent to the global analytic SAP of its associated Hankel system…

Foias–Williams conjecture. There exists a Hankel operator $H_g$ with symbol $g$ such that $T(H_g)$ is polynomially bounded and is not similar to a contraction.

The spectral datum of a Hankel operator consists of the type of its spectral measure and its multiplicity function. For compact Hankel operators, Gérard and Grellier constructed a…

Zhu's conjecture. The difference between the Segal–Bargmann space, where $H_f$ is compact if and only if $H_{\bar f}$ is compact for bounded $f$, and the Bergman and Hardy spaces,…

Let $H^1$ be the Hardy space, and let $T(a)$ and $H(b)$ denote the Toeplitz and Hankel operators with symbols $a$ and $b$, respectively. Toeplitz+Hankel decomposition conjecture. I…

Index relation conjecture. If one of the operators $W(a)+H(b)$ or $W(a)-H(b)$ is Fredholm, then the other is Fredholm as well, and the displayed index relation holds. This would ex…

Let $G$ be the algebra of symbols used for the Wiener–Hopf operators, let $W(a)$ denote the Wiener–Hopf operator with symbol $a$, and let $H(a)$ denote the corresponding Hankel ope…