Non-commutativity of exponential spectrum

2015/10/27 by Klaja, Hubert, Ransford, Thomas
#Algebraic Topology (math.AT) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1510.08109

Abstract

In a Banach algebra, the spectrum satisfies σ(ab)∖\0\ = σ(ba)∖\0\ for each pair of elements a,b. We show that this is no longer true for the exponential spectrum, thereby solving a problem open since 1992. Our proof depends on the fact that the homotopy group π₄(GL₂(\mathbb C)) is non-trivial.

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