Differential geometry of partial isometries and partial unitaries

• Autores: Andruchow, Esteban; Corach, Gustavo
• Año de publicación: 2004
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: PARTIAL ISOMETRIES; UNITARY
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

Let a be a C^*-algebra. In this paper the sets I of partial isometries and I_Δ ⊂ I of partial unitaries (i.e., partial isometries which commute with their adjoints) are studied from a differential geometric point of view. These sets are complemented submanifolds of A. Special attention is paid to geodesic curves. The space I is a homogeneous reductive space of the group U_A x U_A, where U_a denotes the unitary group of A, and geodesics are computed in a standard fashion. Here we study the problem of the existence and uniqueness of geodesics joining two given endpoints. The space I_Δ is not homogeneous, and therefore  a completely different treatment is given. A  principal bundle with base space I_Δ is introduced, and a natural connection in it defined. Additional data, namely certain translating maps, enable one to produce a linear connection in I_Δ, whose geodesics are characterized.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento; Argentina
Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina