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Everything about Commutator subspace
In mathematics, the commutator subspace of a two-sided ideal of bounded linear operators on a separable Hilbert space is the linear subspace spanned by commutators of operators in the ideal with bounded operators. Modern characterisation of the commutator subspace is through the Calkin correspondence and it involves the invariance of the Calkin sequence space of an operator ideal to taking Cesàro means. This explicit spectral characterisation reduces problems and questions about commutators and traces on two-sided ideals to problems and conditions on sequence spaces. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Commutator subspaceA 5-minute orientation
- Pick up a classic book: Commutative AlgebraThe most-reprinted book on the subject
- Read the landmark paper: A Least-Squares Commutator in the Iterative Subspace Method for Accelerating Self-Consistent Field ConvergenceCited 10 times
- Go sideways: Singular traceA closely related topic
- Go sideways: Calkin correspondenceA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
📚 Books worth reading
Commutative AlgebraIrena Peeva · 2013
Perturbation theory for linear operatorsTosio Katō · 1966
Principles of functional analysisMartin Schechter · 1971
Coding the MatrixPhilip N. Klein · 2013- 📕Von Neumann algebras in SibiuInternational Workshop on Free Probabilities, Operator Spaces and von Neumann Algebras (2007 Sibiu, Romania) · 2008
- 📕Hilbert space and quantum mechanicsFranco Gallone · 2015
Excursions in Harmonic Analysis, Volume 1Travis D. Andrews · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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