The invariant subspaces of $S\oplus S^*$

preprint2020arXivOpen access

Using the tools of Sz.-Nagy--Foias theory of contractions, we describe in detail the invariant subspaces of the operator $S\oplus S^*$ , where $S$ is the unilateral shift on a Hilbert space. This answers a question of Câmara and Ross.

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The invariant subspaces of $S\oplus S^*$

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The invariant subspaces of S⊕S∗ S\oplus S^* S⊕S∗

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The invariant subspaces of $S\oplus S^*$