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arXiv · 1612.05821

Invariant subspaces for commuting operators in a real Banach space

Victor Lomonosov·Victor Shulman
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Abstract

It is proved that a commutative algebra $A$ of operators in a reflexive real Banach space has an invariant subspace if each operator $T\in A$ satisfies the condition $$\|1- \varepsilon T^2\|_e \le 1 + o(\varepsilon) \text{ when } \varepsilon\searrow 0,$$ where $\|\cdot\|_e$ is the essential norm. This implies the existence of an invariant subspace for every commutative family of essentially selfadjoint operators in a real Hilbert space.

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Victor Lomonosov, Victor Shulman. 2016-12-17. Invariant subspaces for commuting operators in a real Banach space. https://arxiv.org/abs/1612.05821

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