5 papers
Decomposibility and norm convergence properties in finite von Neumann algebras
Ken Dykema, Joseph Noles, Dmitriy Zanin
We study Schur-type upper triangular forms for elements, T, of von Neumann algebras equipped with faithful, normal, tracial states. These were introduced in a paper of Dykema, Suko…
Weak type operator Lipschitz and commutator estimates for commuting tuples
Martijn Caspers, Fedor Sukochev, Dmitriy Zanin
Let be a Lipschitz function. If is a bounded self-adjoint operator and if are commuting bounded self-adjoint operators such th…
Catalysis in the trace class and weak trace class ideals
Guillaume Aubrun, Fedor Sukochev, Dmitriy Zanin
Given operators in some ideal in the algebra of all bounded operators on a separable Hilbert space , can we give conditions guaranteeing the…
Dixmier traces generated by exponentiation invariant generalised limits
Fedor Sukochev, Alexandr Usachev, Dmitriy Zanin
We define a new class of singular positive traces on the ideal of generated by exponentiation invariant generalized limits. We prove that this new cl…
On the distinction between the classes of Dixmier and Connes-Dixmier traces
Fedor Sukochev, Alexandr Usachev, Dmitriy Zanin
In the present paper we prove that the classes of Dixmier and Connes-Dixmier traces differ even on the Dixmier ideal . We construct a Marcinkiewicz space $\m…