Balanced pairs of operators and their relative index

2016/05/28 by Manuilov, Vladimir
#46L80 #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1605.08843

Abstract

We show that the K₁ group of a C*-algebra A can be defined as homotopy classes of pairs, called balanced, of not necessarily unitary matrices over A that have equal defects from being unitary. We also consider pairs of order zero pseudodifferential operators, not necessarily elliptic, with symbols being a balanced pair. A relative index is defined for such pairs of operators and it equals the topological index of the pair of their symbols.

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