Definition (Graph of an Operator) The graph of an operator TTT in a Hilbert space H\hilb{H}H is the set of all pairs (x,y)∈H×H(x,y) \in \hilb{H}\times\hilb{H}(x,y)∈H×H where xxx lies in the domain of TTT and y=Txy=Txy=Tx.
Definition (Graph of an Operator)
The graph of an operator TTT in a Hilbert space H\hilb{H}H is the set of all pairs (x,y)∈H×H(x,y) \in \hilb{H}\times\hilb{H}(x,y)∈H×H where xxx lies in the domain of TTT and y=Txy=Txy=Tx.