Miscellaneous on Commutants mod Normed Ideals and Quasicentral Modulus I

2020/08/16 by Dan-Virgil Voiculescu, Voiculescu, Dan-Virgil
Mathematics · #46L87 #47B10 #FOS: Mathematics #Functional Analysis (math.FA) #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Primary: 47A55: Secondary: 46L80 #math.FA #math.KT #math.OA #msc:46L80 #msc:46L87 #msc:47B10

paper · pdf · doi:10.48550/arxiv.2008.06990

14 pages minor corrections

arxiv created 2021/07/15 · arxiv updated 2021/07/16

Abstract

We define commutants mod normed ideals associated with compact smooth manifolds with boundary. The results about the K-theory of these operator algebras include an exact sequence for the connected sum of manifolds, derived from the Mayer-Vietoris sequence. We also make a few remarks about bicommutants mod normed ideals and about the quasicentral modulus for the quasinormed p-Schatten-von Neumann classes 0 < p < 1.

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