Unitary equivalence ($B=UA{U}^{-1}$)

Two operators on Hilbert spaces are unitarily equivalent if a unitary operator maps their operator domains onto one another and intertwines their actions. Their spectra and eigenvalue multiplicities then agree. For nonnegative self-adjoint operators it suffices that the unitary maps their closed quadratic form domains onto one another and preserves the forms, since the associated operator is determined by the form.