Exercise 7.A.7

Answers

Proof. Keep in mind that, by 7.6 (c), ${(ST)}^{∗} = T^{∗} S^{∗}$ .

Suppose $ST$ is self adjoint. Then

ST = {(ST)}^{∗} = T^{∗} S^{∗} = TS .

Conversely, suppose $ST = TS$ . Then

ST = TS = T^{∗} S^{∗} = {(ST)}^{∗} .

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2017-10-06 00:00