Geodesic
Remarks on Invariant Subspace Lattices
Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 639-643

Voir la notice de l'article provenant de la source Cambridge University Press

If A is a bounded linear operator on an infinite-dimensional complex Hilbert space H, let lat A denote the collection of all subspaces of H that are invariant under A; i.e., all closed linear subspaces M such that x ∈ M implies (Ax) ∈ M. There is very little known about the question: which families F of subspaces are invariant subspace lattices in the sense that they satisfy F = lat A for some A? (See [5] for a summary of most of what is known in answer to this question.) Clearly, if F is an invariant subspace lattice, then {0} ∈ F, H ∈ F and F is closed under arbitrary intersections and spans. Thus, every invariant subspace lattice is a complete lattice. 
Rosenthal, Peter. Remarks on Invariant Subspace Lattices. Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 639-643. doi: 10.4153/CMB-1969-082-1
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[1] 1. Bernstein, A.R. and Robinson, A., Solution to an invariant subspace problem of K. T. Smith and P. R. Halmos. Pacific J. Math. 16 (1966) 421–431. Google Scholar

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[5] 5. Rosenthal, Peter, Examples of invariant subspace lattices. Duke Math. J. (to appear). Google Scholar

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