IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Geometry of the left action of the p-Schatten groups.
Autor/es:
MAR√ćA EUGENIA DI IORIO Y LUCERO
Revista:
BANACH JOURNAL OF MATHEMATICAL ANALYSIS
Editorial:
BANACH MATHEMATICAL RESEARCH GROUP
Referencias:
Año: 2012
ISSN:
1735-8787
Resumen:
Abstract. Let H be an in nite dimentional Hilbert space, Bp (H) the p-Schatten class of H and Up (H) be the Banach-Lie group of unitary operatorswhich are p-Schatten perturbations of the identity. Let A be a bounded self-adjoint operator in H. We show thatOA := UA : U 2 Up (H)is a smooth submanifold of the afinne space A + Bp (H) if only if A has closedrange. Futhermore, it is a homogeneous reductive space of Up (H). We intro-duce two metrics: one via the ambient Finsler metric induced as a submanifoldof A + Bp (H), the other, by means of the quotient Finsler metric providedby the homogeneous space structure. We show that OA is a complete metricspace with the recti able distance of these metrics.