If "T" is non-negative without being strictly positive, then the inverse of "B" cannot be defined, but the Moore–Penrose pseudoinverse "B"+ can be. In that case, the operator is a partial isometry, that is, a unitary operator from the range of "T" to itself. This can then be extended to a unitary operator "U" on the whole space by setting it equal to the identity on the kernel of "T". More generally, this is true on an infinite-dimensional Hilbert space if, in addition, "T" has closed range. In general, if "A", "B" are closed and densely defined operators on a Hilbert space "H", and "A* A" = "B* B", then "A = UB" where "U" is a partial isometry.