Controlling almost-invariant halfspaces in both real and complex settings

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dc.contributor.authorTcaciuc, Adi
dc.contributor.authorWallis, Ben
dc.date.accessioned2020-12-16
dc.date.accessioned2022-05-31T01:43:00Z
dc.date.available2022-05-31T01:43:00Z
dc.date.issued2017
dc.description.abstractIf T is a bounded linear operator acting on an infinite-dimensional Banach space X, we say that a closed subspace Y of X of both infinite dimension and codimension is an almost-invariant halfspace (AIHS) under T whenever TY⊆Y+E for some finite-dimensional subspace E, or, equivalently, (T+F)Y⊆Y for some finite-rank perturbation F:X→X. We discuss the existence of AIHS’s for various restrictions on E and F when X is a complex Banach space. We also extend some of these and other results in the literature to the setting where X is a real Banach space instead of a complex one.
dc.format.extent445.39KB
dc.format.mimetypePDF
dc.identifier.citationTcaciuc, Adi & Wallis, Ben. (2017). Controlling almost-invariant halfspaces in both real and complex settings. Integral Equations and Operator Theory 87, 117–137. https://doi.org/10.1007/s00020-016-2339-5
dc.identifier.doihttps://doi.org/10.1007/s00020-016-2339-5
dc.identifier.urihttps://hdl.handle.net/20.500.14078/2100
dc.languageEnglish
dc.language.isoen
dc.rightsAll Rights Reserved
dc.subjectfunctional analysis
dc.subjectBanach spaces
dc.subjectspectrum
dc.subjectlocal spectral theory
dc.subjectinvariant subspaces
dc.titleControlling almost-invariant halfspaces in both real and complex settings
dc.typeArticle Post-Print
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