Dmitriy Zanin

Traces on symmetrically normed operator ideals

Abstract 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 semi-finite von Neumann algebras.

Johnson–Schechtman and Khintchine inequalities in noncommutative probability theory

We prove disjointification inequalities due to Johnson and Schechtman for noncommutative random variables independent in the sense of Junge and Xu. In the same setting, we also prove noncommutative Khinchine inequalities. These inequalities are proved both for symmetric operator spaces and for modulars.

A decomposition theorem in II1-factors

Building on results of Haagerup and Schultz, we decompose an arbitrary operator in a diffuse, finite von Neumann algebra into the sum of a normal operator and an s.o.t.-quasinilpotent operator. We also prove an analogue of Weyls inequality relating eigenvalues and singular values for operators in a diffuse, finite von Neumann algebra.

On the distinction between the classes of Dixmier and Connes-Dixmier traces

In the present paper we prove that the classes of Dixmier and Connes-Dixmier traces differ even on the Dixmier ideal

An upper triangular decomposition theorem for some unbounded operators affiliated to II 1 -factors

\mathcal M_{1,\infty}

Algebras of Log-Integrable Functions and Operators

. We construct a Marcinkiewicz space

DIXMIER TRACES GENERATED BY EXPONENTIATION INVARIANT GENERALISED LIMITS

\mathcal M_\psi

Trace formulas for a class of non-Fredholm operators: A review

and a positive operator

Krein's trace theorem revisited

T\in \mathcal M_\psi

Decomposability and Norm Convergence Properties in Finite von Neumann Algebras

which is Connes-Dixmier measurable but which is not Dixmier measurable.