Controlling almost-invariant halfspaces in both real and complex settings

dc.contributor.author	Tcaciuc, Adi
dc.contributor.author	Wallis, Ben
dc.date.accessioned	2020-12-16
dc.date.accessioned	2022-05-31T01:43:00Z
dc.date.available	2022-05-31T01:43:00Z
dc.date.issued	2017
dc.description.abstract	If 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.extent	445.39KB
dc.format.mimetype	PDF
dc.identifier.citation	Tcaciuc, 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.doi	https://doi.org/10.1007/s00020-016-2339-5
dc.identifier.uri	https://hdl.handle.net/20.500.14078/2100
dc.language	English
dc.language.iso	en
dc.rights	All Rights Reserved
dc.subject	functional analysis
dc.subject	Banach spaces
dc.subject	spectrum
dc.subject	local spectral theory
dc.subject	invariant subspaces
dc.title	Controlling almost-invariant halfspaces in both real and complex settings	en
dc.type	Article Post-Print

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