Abstract
Let \(\mathcal{A}\) be a unital C*-algebra and G the group of units of \(\mathcal{A}\). A geometrical study of the action of G over the set \(\mathcal{A}\) + of all positive elements of \(\mathcal{A}\) is presented. The orbits of elements with closed range by this action are provided with a structure of differentiable homogeneous space with a natural connection. The orbits are partitioned in ''components'' which also have a rich geometrical structure.
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Corach, G., Maestripieri, A. & Stojanoff, D. Orbits of Positive Operators from a Differentiable Viewpoint. Positivity 8, 31–48 (2004). https://doi.org/10.1023/B:POST.0000023202.40428.a8
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DOI: https://doi.org/10.1023/B:POST.0000023202.40428.a8