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Following András's lead: Halmos quotes Segal (1951) where the multiplication operator version appears as Lemma 4.2. Segal in turn refers to Plesner-Rokhlin (1946) and Wecken (1939).

Plesner-Rokhlin have it as Theorem 1, page 137: "Any cyclic operator $A$ is isomorphic to $K_\rho$", where they defined $K_\rho F(\xi)=\xi F(\xi)$ on $L^2(\rho)$ (unattributed).

Wecken on the other hand only quotes (a version of) it inside a proof, page 432, with attribution to Stone (1932), Theorem 7.10. There the buck seems to stop.

Following András's lead: Halmos quotes Segal (1951) where the multiplication operator version appears as Lemma 4.2. Segal in turn refers to Plesner-Rokhlin (1946) and Wecken (1939).

Plesner-Rokhlin have it as Theorem 1, page 137: "Any cyclic operator $A$ is isomorphic to $K_\rho$", where they defined $K_\rho F(\xi)=\xi F(\xi)$ on $L^2(\rho)$ (unattributed).

Wecken on the other hand only quotes (a version of) it inside a proof, page 432, with attribution to Stone (1932), Theorem 7.10. There the buck seems to stop.

Following András's lead: Halmos quotes Segal (1951) where the multiplication operator version appears as Lemma 4.2. Segal in turn refers to Plesner-Rokhlin (1946) and Wecken (1939).

Plesner-Rokhlin have it as Theorem 1, page 137: "Any cyclic operator $A$ is isomorphic to $K_\rho$", where they defined $K_\rho F(\xi)=\xi F(\xi)$ on $L^2(\rho)$ (unattributed).

Wecken on the other hand only quotes (a version of) it inside a proof, page 432, with attribution to Stone (1932), Theorem 7.10.

Following András's lead: Halmos quotes Segal (1951) where the multiplication operator version appears as Lemma 4.2. Segal in turn refers to Plesner-Rokhlin (1946) and Wecken (1939).

Plesner-Rokhlin have it as Theorem 1, page 137: "Any cyclic operator $A$ is isomorphic to $K_\rho$", where they defined $K_\rho F(\xi)=\xi F(\xi)$ on $L^2(\rho)$ (unattributed).

Wecken on the other hand only quotes (a version of) it inside a proof, page 432, with attribution to Stone (1932), Theorem 7.10. There the buck seems to stop.

Following András's lead: Halmos quotes Segal (1951) where the multiplication operator version appears as Lemma 4.2. Segal in turn attributes it to Plesner-Rokhlin (1946) where it appears as Theorem 1, p. 137 ("Any cyclic operator $A$ is isomorphic to $K_\rho$", where they defined $K_\rho F(\xi)=\xi F(\xi)$ on $L^2(\rho)$).

Following András's lead: Halmos quotes Segal (1951) where the multiplication operator version appears as Lemma 4.2. Segal in turn refers to Plesner-Rokhlin (1946) and Wecken (1939).

Plesner-Rokhlin have it as Theorem 1, page 137: "Any cyclic operator $A$ is isomorphic to $K_\rho$", where they defined $K_\rho F(\xi)=\xi F(\xi)$ on $L^2(\rho)$ (unattributed).

Wecken on the other hand only quotes (a version of) it inside a proof, page 432, with attribution to Stone (1932), Theorem 7.10.