Geodesic
A Note on the Adjoint of the Product of Operators
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 39-45

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Cordes and Labrousse ([2] p. 697), and Kaniel and Schechter ([6] p. 429) showed that if S and T are domain-dense closed linear operators on a Hilbert space H into itself, the range of S is closed in H and the codimension of the range of S is finite, then, (TS)* = S * T *. With a somewhat different approach and more restricted condition on S, the same assertion was obtained by Holland [5] recently, that S is a bounded everywhere-defined linear operator whose range is a closed subspace of finite codimension in H. 
Lin, Chia-Shiang. A Note on the Adjoint of the Product of Operators. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 39-45. doi: 10.4153/CMB-1970-007-6
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