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arXiv · 2412.19316

A note on common complements

Esteban Andruchow·Eduardo Chiumiento
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Abstract

We discuss the structure of the set $\Delta$ consisting of pairs of closed subspaces that have a common complement in a Hilbert space previously studied by Lauzon and Treil (J. Funct. Anal. 212: 500--512, 2004). We prove that $\Delta$ is the base space of a real analytic fiber bundle constructed in terms of geometric objects associated to the Grassmann manifold. As a consequence we determine the homotopy type of $\Delta$.

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Esteban Andruchow, Eduardo Chiumiento. 2024-12-26. A note on common complements. https://arxiv.org/abs/2412.19316

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