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Let be a unital C-algebra. Given a faithful representation in a Hilbert space , the set of positive invertible elements can be thought of as the set of inner products in , related to , which are equivalent to the original inner product. The set has a rich geometry, it is a homogeneous space of the invertible group of , with an invariant Finsler metric. In the present paper we study the tangent bundle of , as a homogeneous Finsler space of a natural group of invertible matrices in , identifying with the Poincaré half-space of ,
We show that has properties similar to those of a space of non-positive constant curvature.
Cite this article
Esteban Andruchow, Gustavo Corach, Lázaro Recht, The Poincaré half-space of a C-algebra. Rev. Mat. Iberoam. 35 (2019), no. 7, pp. 2187–2219DOI 10.4171/RMI/1117