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Published in:
2018 | OriginalPaper | Chapter
Beyond fractality: piecewise fractal and quasifractal algebras
Author : Steffen Roch
Published in: The Diversity and Beauty of Applied Operator Theory
Publisher: Springer International Publishing
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Fractality is a property of C*-algebras of approximation sequences with several useful consequences: for example, if (An) is a sequence in a fractal algebra, then the pseudospectra of the An converge in the Hausdorff metric. The fractality of a separable algebra of approximation sequences can always be forced by a suitable restriction. This observation leads to the question to describe the possible fractal restrictions of a given algebra. In this connection we define two classes of algebras beyond the class of fractal algebras (piecewise fractal and quasifractal algebras), give examples for algebras with these properties, and present some first results on the structure of quasifractal algebras (being continuous fields over the set of their fractal restrictions).