Commutator subspace (original) (raw)

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 (more resolvable) problems and conditions on sequence spaces.