A note on geodesics of projections in the Calkin algebra
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
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Birkhauser Verlag Ag
2024
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| Acceso en línea: | http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1802 |
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I71-R177-UNGS-18022024-12-23T13:21:45Z A note on geodesics of projections in the Calkin algebra Andruchow, Esteban Calkin algebra Geodesics of projections Projections 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. 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. 2024-12-23T13:21:45Z 2024-12-23T13:21:45Z 2020 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion Andruchow, E. (11-2020). A note on geodesics of projections in the Calkin algebra. Archiv Der Mathematik, 115(5), 545-553. 0003-889X http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1802 eng http://dx.doi.org/10.1007/s00013-020-01509-5 info:eu-repo/semantics/restrictedAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Birkhauser Verlag Ag Archiv Der Mathematik. Nov. 2020; 115(5): 545-553 https://link.springer.com/journal/13/volumes-and-issues/115-5 |
| institution |
Universidad Nacional de General Sarmiento |
| institution_str |
I-71 |
| repository_str |
R-177 |
| collection |
Repositorio Institucional Digital de Acceso Abierto (UNGS) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| topic |
Calkin algebra Geodesics of projections Projections |
| spellingShingle |
Calkin algebra Geodesics of projections Projections Andruchow, Esteban A note on geodesics of projections in the Calkin algebra |
| topic_facet |
Calkin algebra Geodesics of projections Projections |
| description |
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. |
| format |
Artículo Artículo publishedVersion |
| author |
Andruchow, Esteban |
| author_facet |
Andruchow, Esteban |
| author_sort |
Andruchow, Esteban |
| title |
A note on geodesics of projections in the Calkin algebra |
| title_short |
A note on geodesics of projections in the Calkin algebra |
| title_full |
A note on geodesics of projections in the Calkin algebra |
| title_fullStr |
A note on geodesics of projections in the Calkin algebra |
| title_full_unstemmed |
A note on geodesics of projections in the Calkin algebra |
| title_sort |
note on geodesics of projections in the calkin algebra |
| publisher |
Birkhauser Verlag Ag |
| publishDate |
2024 |
| url |
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1802 |
| work_keys_str_mv |
AT andruchowesteban anoteongeodesicsofprojectionsinthecalkinalgebra AT andruchowesteban noteongeodesicsofprojectionsinthecalkinalgebra |
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1824528739061465088 |