2011/08/12 by F. Sukochev, Sukochev, F., D. Zanin +1
Mathematics · #46L52 #47B10 #47L20 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L52 #msc:47B10 #msc:47L20
paper · pdf · doi:10.48550/arxiv.1108.2598
submitted to Crelle
arxiv created 2011/08/12 · arxiv updated 2011/08/15
For every symmetrically normed ideal E of compact operators, we give a criterion for the existence of a continuous singular trace on E. We also give a criterion for the existence of a continuous singular trace on E which respects Hardy-Littlewood majorization. We prove that the class of all continuous singular traces on E is strictly wider than the class of continuous singular traces which respect Hardy-Littlewood majorization. We establish a canonical bijection between the set of all traces on E and the set of all symmetric functionals on the corresponding sequence ideal. Similar results are also proved in the setting of semifinite von Neumann algebras.