Projective spaces of aC *-algebra |
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Authors: | E. Andruchow G. Corach D. Stojanoff |
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Affiliation: | (1) Instituto de Ciencias, UNGS, San Miguel, Argentina;(2) Depto. de Matemática, FCEN-UBA, Buenos Aires, Argentina;(3) Instituto Argentino de Matemática, Buenos Aires, Argentina;(4) Depto. de Matemática, FCE-UNLP, La Plata, Argentina;(5) Instituto Argentino de Matemática, Buenos Aires, Argentina |
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Abstract: | Based on the projective matrix spaces studied by B. Schwarz and A. Zaks, we study the notion of projective space associated to a C*-algebraA with a fixed projectionp. The resulting spaceP(p) admits a rich geometrical structure as a holomorphic manifold and a homogeneous reductive space of the invertible group ofA. Moreover, several metrics (chordal, spherical, pseudo-chordal, non-Euclidean-in Schwarz-Zaks terminology) are considered, allowing a comparison amongP(p), the Grassmann manifold ofA and the space of positive elements which are unitary with respect to the bilinear form induced by the reflection =2p–1. Among several metrical results, we prove that geodesics are unique and of minimal length when measured with the spherical and non-Euclidean metrics.Partially supported by UBACYT TW49 and TX92, PIP 4463 (CONICET) and ANPCYT PICT 97-2259 (Argentina) |
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Keywords: | Primary 46L05 58B20 |
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