5 problems

Self-adjointness conjecture. $T$ is self-adjoint.

Let $\mathfrak M:=\{A^{(1)},\ldots,A^{(n)}\}$ be a finite subset of the positive bounded self-adjoint operators $\mathfrak S^{+}$ on a Hilbert space $\mathscr H$, let $S$ be the pa…

Let $A$ be a densely defined, lower semi-bounded symmetric operator on a Hilbert space. Neumann's conjecture. The operator $A$ has a lower semi-bounded self-adjoint extension that…

Let $A$ be a closed semi-bounded symmetric operator, let ${\bf A}$ denote the associated operator, and let ${\bf A}_F$ be its Friedrichs self-adjoint extension. For…

Let $A$ be a self-adjoint operator whose spectrum is separated into two subsets $4\sigma$ and $\Sigma4$ at distance $d>0$, and let $V$ be an off-diagonal perturbation. Define the m…