Commutator structure of operator ideals

DOI10.1016/S0001-8708(03)00141-5zbMath1103.47054OpenAlexW2050399503WikidataQ56689642 ScholiaQ56689642MaRDI QIDQ1826880

Tadeusz Figiel, Gary Weiss, Mariusz Wodzicki, Kenneth J. Dykema

Publication date: 6 August 2004

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0001-8708(03)00141-5

Mathematics Subject Classification ID

Normed linear spaces and Banach spaces; Banach lattices (46B99) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Abstract operator algebras on Hilbert spaces (47L30) Commutators, derivations, elementary operators, etc. (47B47) Operator ideals (47L20)

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Cites Work

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• Excision in cyclic homology and in rational algebraic K-theory
• Non-commutative differential geometry
• Value of the Steinitz constant
• Commutators of Hilbert-Schmidt operators II
• On the existence of quasicentral approximate units relative to normed ideals. I
• Commutators of Hilbert-Schmidt operators. I
• Trace-class operators and commutators
• Structure of commutators of operators
• Hardy-Littlewood majorants in function spaces
• Ideals of compact operators on Hilbert space
• On commutators in ideals of compact operators
• Indices for the Orlicz spaces
• Commutators and compressions
• A unified theory of regularly varying sequences
• The cross-space of linear transformations. III
• Two-sided ideals and congruences in the ring of bounded operators in Hilbert space
• Traces on Irregular Ideals
• The Steinitz constant of the plane.
• Unusual Traces on Operator Ideals
• Commutators of compact operators.
• On the Structure of Principal Ideals of Operators
• Spectral characterization of sums of commutators I
• Construction de triplets spectraux à partir de modules de Fredholm
• Traces of commutators of Schatten-von Neumann class operators.
• The Steinitz theorem on rearrangement of series for nuclear spaces.
• On Symmetric Sequence Spaces
• Indices of Function Spaces and their Relationship to Interpolation
• Rearrangement Inequalities
• Inequalities between the Two Kinds of Eigenvalues of a Linear Transformation
• Remark on Weyl's Note “Inequalities Between the Two Kinds of Eigenvalues of a Linear Transformation”
• Maximum Properties and Inequalities for the Eigenvalues of Completely Continuous Operators
• An Inequality for Rearrangements
• Commutators of Operators, II