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Metric and homogeneous structure of closed range operators

Gustavo Corach·Alejandra Maestripieri·Mostafa Mbekhta
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Abstract

Let $\CR$ be the set of all bounded linear operators between Hilbert spaces $\cH, \cK$. This paper is devoted to the study of the topological properties of $\CR$ if certain natural metrics are considered on it. We also define an action of the group $\G_\cH\times\G_\cK$ on $\CR$ and determine the orbits of this action. These orbits determine a stratification of the set of Fredholm and semi-Fredholm operators. Finally, we calculate the distance, with respect to some of the metrics mentioned above, between different orbits of $\CR$.

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Gustavo Corach, Alejandra Maestripieri, Mostafa Mbekhta. 2005-09-14. Metric and homogeneous structure of closed range operators. https://arxiv.org/abs/math/0509328

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