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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Guardado en:
Detalles Bibliográficos
Publicado: 2010
Materias:
Dual frames
Pseudoframes
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0378620X_v67_n4_p451_Andruchow
http://hdl.handle.net/20.500.12110/paper_0378620X_v67_n4_p451_Andruchow
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_0378620X_v67_n4_p451_Andruchow
record_format dspace
spelling paper:paper_0378620X_v67_n4_p451_Andruchow2023-06-08T15:40:26Z Topology and smooth structure for pseudoframes 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. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0378620X_v67_n4_p451_Andruchow 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
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.
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
publishDate 2010
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0378620X_v67_n4_p451_Andruchow
http://hdl.handle.net/20.500.12110/paper_0378620X_v67_n4_p451_Andruchow
_version_ 1768544962302967808

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