Controlling almost-invariant halfspaces in both real and complex settings
functional analysis, Banach spaces, spectrum, local spectral theory, invariant subspaces
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.
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
All Rights Reserved