Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Commutator subspace
open-in-new
<p>In mathematics, the commutator subspace of a two-sided <a href="/facts/Ideal_(ring_theory)/vCvytduX">ideal</a> of <a href="/facts/Linear_operators/Q1PBKNVV">bounded linear operators</a> on a separable <a href="/facts/Hilbert_space/aDFMh4lV">Hilbert space</a> is the linear subspace spanned by <a href="/facts/Commutator/eYxzFmFY">commutators</a> of operators in the ideal with bounded operators. Modern characterisation of the commutator subspace is through the <a href="/facts/Calkin_correspondence/8Lhv2xDg">Calkin correspondence</a> and it involves the invariance of the Calkin sequence space of an operator ideal to taking <a href="/facts/Ces%C3%A0ro_mean/ttbvyscp">Cesàro means</a>. This explicit spectral characterisation reduces problems and questions about commutators and <a href="/facts/Singular_trace/S4xkdjCI">traces</a> on two-sided ideals to (more resolvable) problems and conditions on sequence spaces. </p>