Commutants mod normed ideals

Dan-Virgil Voiculescu ()
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Dan-Virgil Voiculescu: University of California at Berkeley, Department of Mathematics

A chapter in Advances in Noncommutative Geometry, 2019, pp 585-606 from Springer

Abstract: 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.

Date: 2019
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DOI: 10.1007/978-3-030-29597-4_10

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