6 problems

Let $H$ be a $\mathcal{PT}$-symmetric Hamiltonian with unbroken $\mathcal{PT}$-symmetry, and let its eigenstates be the corresponding eigenfunctions. A sequence is of the first typ…

Conjecture on unbroken $\mathcal{PT}$ symmetry. The eigenstates of a $\mathcal{PT}$-symmetric Hamiltonian $H$ with unbroken $\mathcal{PT}$ symmetry form a first type sequence.

Connectedness conjecture. The set ${\mathbb G}{\mathbb I}_n({\cal K},J)$ is connected. The conjecture is motivated by Cayley-transform arguments and homotopy methods, but the suppl…

Let a J-isometry be an unbounded $J$-unitary operator without a Real symmetry, and let the global signature be the associated integer-valued invariant. Global-signature labelling c…

Vanishing-norm conjecture. For $\sigma=-p-2$ and $0\leq L\leq p-1$, the norm of the singular solution vanishes, just as the norm of the regular solution does:

In BRST theory, let the spatial dsp-decomposition be the decomposition of the relevant BRST structure used to analyse the operator cohomology. Spatial dsp-decomposition conjecture.…