The Uniqueness of the Adjoint Operation. III

Let H be a complex, infinite-dimensional Hilbert space with inner pr (•,•)• Let B(H) denote the set of operators on H (i.e. bounded linear transformations of H into itself) and let GL(H) denote the set of invertible operators. If T e B(H) then T is positive or equivalently T > 0 means that ( Tx, x) > 0 for all x e H. The purpose of this paper is to prove the following result.