Topology and smooth structure for pseudoframes
Given a closed subspace S of a Hilbert space H, we study the sets Fs of pseudo-frames, CFs of commutative pseudo-frames and X{script}s of dual frames for S, via the (well known) one to one correspondence which assigns a pair of operators (F, H) to a frame pair ({fn}n∈ℕ,{hn}n∈ℕ), We prove that, with...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0378620X_v67_n4_p451_Andruchow |
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todo:paper_0378620X_v67_n4_p451_Andruchow2023-10-03T15:33:13Z Topology and smooth structure for pseudoframes Andruchow, E. Antezana, J. Corach, G. Dual frames Pseudoframes Given a closed subspace S of a Hilbert space H, we study the sets Fs of pseudo-frames, CFs of commutative pseudo-frames and X{script}s of dual frames for S, via the (well known) one to one correspondence which assigns a pair of operators (F, H) to a frame pair ({fn}n∈ℕ,{hn}n∈ℕ), We prove that, with this identification, the sets Fs, CFs and X{script}s are complemented submanifolds of B(ℓ2,H) × B(ℓ2,H). We examine in more detail X{script}s, which carries a locally transitive action from the general linear group GL(ℓ2). For instance, we characterize the homotopy theory of X{script}s and we prove that X{script}s is a strong deformation retract both of Fs and CFs; therefore these sets share many of their topological properties. © Springer Basel AG 2010. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0378620X_v67_n4_p451_Andruchow |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Dual frames Pseudoframes |
| spellingShingle |
Dual frames Pseudoframes Andruchow, E. Antezana, J. Corach, G. Topology and smooth structure for pseudoframes |
| topic_facet |
Dual frames Pseudoframes |
| description |
Given a closed subspace S of a Hilbert space H, we study the sets Fs of pseudo-frames, CFs of commutative pseudo-frames and X{script}s of dual frames for S, via the (well known) one to one correspondence which assigns a pair of operators (F, H) to a frame pair ({fn}n∈ℕ,{hn}n∈ℕ), We prove that, with this identification, the sets Fs, CFs and X{script}s are complemented submanifolds of B(ℓ2,H) × B(ℓ2,H). We examine in more detail X{script}s, which carries a locally transitive action from the general linear group GL(ℓ2). For instance, we characterize the homotopy theory of X{script}s and we prove that X{script}s is a strong deformation retract both of Fs and CFs; therefore these sets share many of their topological properties. © Springer Basel AG 2010. |
| format |
JOUR |
| author |
Andruchow, E. Antezana, J. Corach, G. |
| author_facet |
Andruchow, E. Antezana, J. Corach, G. |
| author_sort |
Andruchow, E. |
| title |
Topology and smooth structure for pseudoframes |
| title_short |
Topology and smooth structure for pseudoframes |
| title_full |
Topology and smooth structure for pseudoframes |
| title_fullStr |
Topology and smooth structure for pseudoframes |
| title_full_unstemmed |
Topology and smooth structure for pseudoframes |
| title_sort |
topology and smooth structure for pseudoframes |
| url |
http://hdl.handle.net/20.500.12110/paper_0378620X_v67_n4_p451_Andruchow |
| work_keys_str_mv |
AT andruchowe topologyandsmoothstructureforpseudoframes AT antezanaj topologyandsmoothstructureforpseudoframes AT corachg topologyandsmoothstructureforpseudoframes |
| _version_ |
1807321670973652992 |