Sphere and projective space of a C*-algebra with a faithful state

• Autores: Antúnez, Andrea Carolina
• Año de publicación: 2019
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Demonstratio Mathematica. 2019; 52(1): 410-427; https://www.degruyter.com/journal/key/dema/52/1/html
• Materia: Homogeneous space; Minimal curves; C*-algebra; Projective space; Espacio homogéneo; Curvas mínimas; C*-álgebra; Espacio proyectivoEspaço homogêneo; Curvas mínimas; Álgebra C*; Espaço projetivo
• Institución: Universidad Nacional de General Sarmiento

Fil: Antúnez, Andrea Carolina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
LetAbe a unitalC*-algebra with a faithful state?. We study the geometry of the unit sphereS?={x?A:?(x*x) = 1}and the projective spaceP?=S?/T. These spaces are shown to be smooth manifoldsand homogeneous spaces of the groupU?(A)of isomorphisms acting inAwhich preserve the inner productinduced by?, which is a smooth Banach-Lie group. An important role is played by the theory of operators inBanach spaces with two norms, as developed by M.G. Krein and P. Lax. We define a metric inP?, and provethe existence of minimal geodesics, both with given initial data, and given endpoints.