Some Results and a K-theory Problem about Threshold Commutants mod Normed Ideals

2019/11/17 by Dan-Virgil Voiculescu, Voiculescu, Dan-Virgil
Mathematics · #46L80 #47L20 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Functional Analysis (math.FA) #Primary:47A55 #Secondary: 47A40 #math.FA #msc:46L80 #msc:47A40 #msc:47L20

paper · pdf · doi:10.48550/arxiv.1911.07377

14 pages

openalex publication_date 2019/11/17 · arxiv created 2019/12/01 · arxiv updated 2019/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend to the case of a threshold ideal our result with J. Bourgain about the essential centre of the commutant mod a diagonalization ideal for a n-tuple of commuting Hermitian operators . We also compute the K₀-group of the commutant mod trace-class of a unitary operator with spectrum equal to its essential spectrum. We present the problem of computing the K₁-group for a commutant mod trace-class in its simplest case.

Related

• The essential centre of the mod a diagonalization ideal commutant of an n-tuple of commuting hermitian operators
• K-theory and perturbations of absolutely continuous spectra
• Commutants mod Normed Ideals
• Lebesgue decomposition of functionals and unique preduals for commutants modulo normed ideals
• Miscellaneous on Commutants mod Normed Ideals and Quasicentral Modulus I