Almost-invariant and essentially-invariant halfspaces

Gleb Sirotkin,Ben Wallis

doi:10.1016/j.laa.2016.06.025

Almost-invariant and essentially-invariant halfspaces

Gleb Sirotkin, Ben Wallis

Open Access

https://doi.org/10.1016/j.laa.2016.06.025

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Journal: Linear Algebra and Its Applications	Publication Date: Jun 17, 2016
Citations: 7	License type: elsevier-specific: oa user license

Affiliation: Northern Illinois University

#Infinite-dimensional Banach Space #Infinite-dimensional Space + Show 5 more

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Abstract

In this paper we study sufficient conditions for an operator to have an almost-invariant half-space. As a consequence, we show that if X is an infinite-dimensional complex Banach space then every operator T∈L(X) admits an essentially-invariant half-space. We also show that whenever a closed algebra of operators possesses a common AIHS, then it has a common invariant half-space as well.

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