p-Schatten commutators of projections

• Autores: Andruchow, Esteban; Di Iorio y Lucero, María Eugenia
• Año de publicación: 2021
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Annals of Functional Analysis. 2021; 12(2): 1-20; https://link.springer.com/journal/43034/volumes-and-issues/12-2
• Materia: Projections; Schatten P-Ideals
• Institución: Universidad Nacional de General Sarmiento

Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
Fil: Di Iorio y Lucero, María Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
Let H= H+? H- be a fixed orthogonal decomposition of the complex separable Hilbert space H in two infinite-dimensional subspaces. We study the geometry of the set Pp of selfadjoint projections in the Banach algebra Ap= { A? B(H) : [A, E+] ? Bp(H) } , where E+ is the projection onto H+ and Bp(H) is the Schatten ideal of p-summable operators (1 ? p< ?). The norm in Ap is defined in terms of the norms of the matrix entries of the operators given by the above decomposition. The space Pp is shown to be a differentiable C? submanifold of Ap, and a homogeneous space of the group of unitary operators in Ap. The connected components of Pp are characterized, by means of a partition of Pp in nine classes, four discrete classes, and five essential classes: (1) the first two corresponding to finite rank or co-rank, with the connected components parametrized by these ranks; (2) the next two discrete classes carrying a Fredholm index, which parametrizes their components; (3) the remaining essential classes, which are connected.