[′səb‚nȯr·məl ′äp·ə‚rād·ər] (mathematics) An operator A on a Hilbert spaceHis said to be subnormal if there exists a normal operator B on a Hilbert spaceKsuch thatHis a subspace ofK, the subspaceHis invariant under the operator B, and the restriction of B toHcoincides with A.