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- W4297580462 abstract "We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we show that the same is true for operators which have non-eigenvalues in the boundary of their spectrum. In the Hilbert space, our methods produce perturbations that are also small in norm, improving on an old result of Brown and Pearcy." @default.
- W4297580462 created "2022-09-30" @default.
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- W4297580462 date "2012-08-29" @default.
- W4297580462 modified "2023-10-18" @default.
- W4297580462 title "Every operator has almost-invariant subspaces" @default.
- W4297580462 doi "https://doi.org/10.48550/arxiv.1208.5831" @default.
- W4297580462 hasPublicationYear "2012" @default.
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