Timeline for Addition of essentially self-adjoint operators

4 events

when toggle format	what		by	license	comment
Jun 5, 2011 at 14:18	vote	accept	jsb
Jun 4, 2011 at 10:41	comment	added	Michael Renardy		In the example above D is a core for A and B. It is not a core for A+B.
Jun 4, 2011 at 7:43	comment	added	Dima Shlyakhtenko		It may be helpful to note that the reason counterexamples exist is that the intersection of the two domains may be smaller than each of the domains; and if $A$ is ess. self-adjoint with domain $D$ and $D_0\subset D$ is dense, the closure of the restriction of $A$ to $D_0$ may not coincide with $A$. (If the closure of the restriction of $A$ to $D_0$ is $A$ one sometimes says that $D_0$ is a core for $A$). So your $A+B$ will be ess. self-adjoint if you assume that there is a common core for $A$ and $B$.
Jun 4, 2011 at 7:34	history	answered	Michael Renardy	CC BY-SA 3.0