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Published in:
2018 | OriginalPaper | Chapter
Extension-Restriction Theorems for Algebras of Approximation Sequences
Author : Steffen Roch
Published in: Operator Theory, Operator Algebras, and Matrix Theory
Publisher: Springer International Publishing
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The C∗-algebra $$\mathcal{S}({\mathrm{T}}(C))$$ of the finite sections discretization for Toeplitz operators with continuous generating functions is fairly well understood. Since its description in [3], this algebra serves both as a source of inspiration and as an archetypal example of an algebra generated by an discretization procedure. Moreover, it turns out that every separable C∗-algebra of approximation sequences has a common structure with $$\mathcal{S}({\mathrm{T}}(C))$$ after an extension by compact sequences and a suitable fractal restriction. We explain what this statement means and give a proof.