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arXiv · 1509.07428

Almost-invariant and essentially-invariant halfspaces

Gleb Sirotkin·Ben Wallis
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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 $T\in\mathcal{L}(X)$ 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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Gleb Sirotkin, Ben Wallis. 2015-09-24. Almost-invariant and essentially-invariant halfspaces. https://arxiv.org/abs/1509.07428

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