Quantitative $K$-theory for Banach algebras

Abstract

Quantitative (or controlled) $K$-theory for $C^{\ast }$-algebras was used by Guoliang Yu in his work on the Novikov conjecture, and later developed more formally by Yu together with Hervé Oyono-Oyono. In this paper, we extend their work by developing a framework of quantitative $K$-theory for the class of algebras of bounded linear operators on subquotients (i.e., subspaces of quotients) of $L_p$ spaces. We also prove the existence of a controlled Mayer-Vietoris sequence in this framework.

58 pages, corrections made based on referee's report, accepted for publication in Journal of Functional Analysis

References in corpus (2)

• Quotients of Banach algebras acting on $L^p$-spaces
• Dynamic Asymptotic Dimension: relation to dynamics, topology, coarse geometry, and $C^{\ast }$-algebras

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