Artículo
A note on geodesics of projections in the Calkin algebra
Fecha de publicación:
11/2020
Editorial:
Birkhauser Verlag Ag
Revista:
Archiv Der Mathematik
ISSN:
0003-889X
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Let C(H) = B(H) / K(H) be the Calkin algebra (B(H) the algebra of bounded operators on the Hilbert space H, K(H) the ideal of compact operators, and π: B(H) → C(H) the quotient map), and PC(H) the differentiable manifold of selfadjoint projections in C(H). A projection p in C(H) can be lifted to a projection P∈ B(H) : π(P) = p. We show that, given p, q∈ PC(H), there exists a minimal geodesic of PC(H) which joins p and q if and only if there exist lifting projections P and Q such that either both N(P- Q± 1) are finite dimensional, or both are infinite dimensional. The minimal geodesic is unique if p+ q- 1 has trivial anhihilator. Here the assertion that a geodesic is minimal means that it is shorter than any other piecewise smooth curve γ(t) ∈ PC(H), t∈ I, joining the same endpoints, where the length of γ is measured by ∫ I‖ γ˙ (t) ‖ dt.
Palabras clave:
CALKIN ALGEBRA
,
GEODESICS OF PROJECTIONS
,
PROJECTIONS
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(IAM)
Articulos de INST.ARG.DE MATEMATICAS "ALBERTO CALDERON"
Articulos de INST.ARG.DE MATEMATICAS "ALBERTO CALDERON"
Citación
Andruchow, Esteban; A note on geodesics of projections in the Calkin algebra; Birkhauser Verlag Ag; Archiv Der Mathematik; 115; 5; 11-2020; 545-553
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