Metric and homogeneous structure of closed range operators
Let CR be the set of all bounded linear operators between Hilbert spaces H, κ with closed range. This paper is devoted to the study of the topological properties of CR. if certain natural metrics are considered on it. We also define an action of the group GH × Gκ, on CR and determine the orbits of t...
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todo:paper_03794024_v61_n1_p171_Corach2023-10-03T15:33:25Z Metric and homogeneous structure of closed range operators Corach, G. Maestripieri, A. Mbekhta, M. Closed range Moore-Penrose inverse Partial isometry Positive operators, orbits Semi-Fredholm operators Let CR be the set of all bounded linear operators between Hilbert spaces H, κ with closed range. This paper is devoted to the study of the topological properties of CR. if certain natural metrics are considered on it. We also define an action of the group GH × Gκ, on CR and determine the orbits of this action. These orbits, which are strongly related to the connected components for the topology defined by the metrics mentioned above, determine a stratification of the set of Fredholm and semi-Fredholm operators. Finally, we calculate the distance, with respect to some of the metrics mentioned above, between different orbits of CR. © Copyright by THETA 2009. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03794024_v61_n1_p171_Corach |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Closed range Moore-Penrose inverse Partial isometry Positive operators, orbits Semi-Fredholm operators |
| spellingShingle |
Closed range Moore-Penrose inverse Partial isometry Positive operators, orbits Semi-Fredholm operators Corach, G. Maestripieri, A. Mbekhta, M. Metric and homogeneous structure of closed range operators |
| topic_facet |
Closed range Moore-Penrose inverse Partial isometry Positive operators, orbits Semi-Fredholm operators |
| description |
Let CR be the set of all bounded linear operators between Hilbert spaces H, κ with closed range. This paper is devoted to the study of the topological properties of CR. if certain natural metrics are considered on it. We also define an action of the group GH × Gκ, on CR and determine the orbits of this action. These orbits, which are strongly related to the connected components for the topology defined by the metrics mentioned above, determine a stratification of the set of Fredholm and semi-Fredholm operators. Finally, we calculate the distance, with respect to some of the metrics mentioned above, between different orbits of CR. © Copyright by THETA 2009. |
| format |
JOUR |
| author |
Corach, G. Maestripieri, A. Mbekhta, M. |
| author_facet |
Corach, G. Maestripieri, A. Mbekhta, M. |
| author_sort |
Corach, G. |
| title |
Metric and homogeneous structure of closed range operators |
| title_short |
Metric and homogeneous structure of closed range operators |
| title_full |
Metric and homogeneous structure of closed range operators |
| title_fullStr |
Metric and homogeneous structure of closed range operators |
| title_full_unstemmed |
Metric and homogeneous structure of closed range operators |
| title_sort |
metric and homogeneous structure of closed range operators |
| url |
http://hdl.handle.net/20.500.12110/paper_03794024_v61_n1_p171_Corach |
| work_keys_str_mv |
AT corachg metricandhomogeneousstructureofclosedrangeoperators AT maestripieria metricandhomogeneousstructureofclosedrangeoperators AT mbekhtam metricandhomogeneousstructureofclosedrangeoperators |
| _version_ |
1807319587303194624 |