Strongly continuous unitary group

A strongly continuous unitary group is a family $U(t)$ for all real $t$ that is strongly continuous, obeys the group law, and preserves the Hilbert norm. Its generator is skew-adjoint; conversely, every skew-adjoint operator generates such a group.

An operator $A$ is skew-adjoint when $A^{\ast }=-A$. Both $A$ and $-A$ are then maximal dissipative, and the generated group is unitary.