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Commutants mod normed ideals

In: Advances in Noncommutative Geometry

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  • Dan-Virgil Voiculescu

    (University of California at Berkeley, Department of Mathematics)

Abstract

To Alain Connes’ non-commutative geometry the normed ideals of compact operators are purveyors of infinitesimals. A numerical invariant, the modulus of quasicentral approximation, plays a key role in perturbations from these ideals. New structure is provided by commutants mod normed ideals of n-tuples of operators and by their Calkin algebras. I review the modulus of quasicentral approximation, the relation to invariance of absolutely continuous spectra, to dynamical entropy and the hybrid generalization. I then discuss commutants mod normed ideals, their Banach space duality properties, K-theory aspects, the case of the Macaev ideal. Sample open problems are included.

Suggested Citation

  • Dan-Virgil Voiculescu, 2019. "Commutants mod normed ideals," Springer Books, in: Ali Chamseddine & Caterina Consani & Nigel Higson & Masoud Khalkhali & Henri Moscovici & Guoliang Yu (ed.), Advances in Noncommutative Geometry, pages 585-606, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-29597-4_10
    DOI: 10.1007/978-3-030-29597-4_10
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