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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2010
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| 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 |
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| Sumario: | 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. |
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