Graphs of operators as points in the Grassmann manifold

We study the set $Γ$ of graphs of closed, densely defined operators in a Hilbert space $H$, regarded as a subset of the Grassmann manifold $P(H\times H)$ of orthogonal projections in $H\times H$. We show that the subset $Γ^b$ of graphs of bounded operators is the open unit ball of $P(H\times H)$ cen