Topology and smooth structure for pseudoframes

Esteban Andruchow, Jorge Antezana, Gustavo Corach

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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.
Original languageEnglish
Pages (from-to)451-466
JournalIntegral Equations and Operator Theory
Issue number4
Publication statusPublished - 14 Jul 2010


  • Dual frames
  • Pseudoframes


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