Vladimir Chilin

Continuous derivations on algebras of locally measurable operators are inner

It is proved that every continuous derivation on the *-algebra S(M, τ) of all τ-measurable operators affiliated with a von Neumann algebra M is inner. For every properly infinite von Neumann algebra M, any derivation on the *-algebra S(M, τ) is inner.

Individual ergodic theorems in noncommutative Orlicz spaces

For a noncommutative Orlicz space associated with a semifinite von Neumann algebra, a faithful normal semifinite trace and an Orlicz function satisfying

Derivations with values in quasi-normed bimodules of locally measurable operators

(\delta _2,\Delta _2)

Almost uniform and strong convergences in ergodic theorems for symmetric spaces

(δ2,Δ2)-condition, an individual ergodic theorem is proved.

Isometries and Hermitian operators on complex symmetric sequence spaces

Utilizing the notion of uniform equicontinuity for sequences of functions with the values in the space of measurable operators, we present a non-commutative version of the Banach Principle for L 1 .

Non-trivial Derivations on Commutative Regular Algebras

We prove that every derivation acting on a von Neumann algebra M with values in a quasi-normed bimodule of locally measurable operators affiliated with M is necessarily inner.

A FEW REMARKS IN NON-COMMUTATIVE ERGODIC THEORY

LetA be a commutativeAW*-algebra.We denote by S(A) the *-algebra of measurable operators that are affiliated with A. For an ideal I in A, let s(I) denote the support of I. Let Y be a solid linear subspace in S(A). We find necessary and sufficient conditions for existence of nonzero band preserving derivations from I to Y. We prove that no nonzero band preserving derivation from I to Y exists if either Y ⊂ Aor Y is a quasi-normed solid space. We also show that a nonzero band preserving derivation from I to S(A) exists if and only if the boolean algebra of projections in the AW*-algebra s(I)A is not σ-distributive.

Continuity of derivations of algebras of locally measurable operators

Let