Frames and outer frames for Hilbert C^*-modules

Ljiljana Arambašić; Damir Bakić

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arXiv · 1507.04101

Frames and outer frames for Hilbert C^*-modules

Ljiljana Arambašić·Damir Bakić

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Abstract

The goal of the present paper is to extend the theory of frames for countably generated Hilbert $C^*$-modules over arbitrary $C^*$-algebras. In investigating the non-unital case we introduce the concept of outer frame as a sequence in the multiplier module $M(X)$ that has the standard frame property when applied to elements of the ambient module $X$. Given a Hilbert $\A$-module $X$, we prove that there is a bijective correspondence of the set of all adjointable surjections from the generalized Hilbert space $\ell^2(\A)$ to $X$ and the set consisting of all both frames and outer frames for $X$. Building on a unified approach to frames and outer frames we then obtain new results on dual frames, frame perturbations, tight approximations of frames and finite extensions of Bessel sequences.

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BibTeX RIS

Ljiljana Arambašić, Damir Bakić. 2015-07-15. Frames and outer frames for Hilbert C^*-modules. https://arxiv.org/abs/1507.04101

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