53 research outputs found
Non Commutative Arens Algebras and their Derivations
Given a von Neumann algebra with a faithful normal semi-finite trace
we consider the non commutative Arens algebra and the related algebras
and
which are proved to be complete metrizable locally
convex *-algebras. The main purpose of the present paper is to prove that any
derivation of the algebra is inner and all
derivations of the algebras and
are spatial and implemented by elements of Comment: 19 pages. Submitted to Journal of Functional analysi
Structure of derivations on various algebras of measurable operators for type I von Neumann algebras
Given a von Neumann algebra denote by and respectively the
algebras of all measurable and locally measurable operators affiliated with
For a faithful normal semi-finite trace on let
(resp. ) be the algebra of all -measurable (resp.
-compact) operators from We give a complete description of all
derivations on the above algebras of operators in the case of type I von
Neumann algebra In particular, we prove that if is of type I
then every derivation on (resp. and ) is inner, and
each derivation on is spatial and implemented by an element from
Comment: 38 page
Boundedness of completely additive measures with application to 2-local triple derivations
We prove a Jordan version of Dorofeev's boundedness theorem for completely
additive measues and use it to show that every (not necessarily linear nor
continuous) 2-local triple derivation on a continuous JBW*-triple is a triple
derivation.Comment: 30 page
Local Derivations on Algebras of Measurable Operators
The paper is devoted to local derivations on the algebra
of -measurable operators affiliated with a von
Neumann algebra and a faithful normal semi-finite trace
We prove that every local derivation on which is
continuous in the measure topology, is in fact a derivation. In the particular
case of type I von Neumann algebras they all are inner derivations. It is
proved that for type I finite von Neumann algebras without an abelian direct
summand, and also for von Neumann algebras with the atomic lattice of
projections, the condition of continuity of the local derivation is redundant.
Finally we give necessary and sufficient conditions on a commutative von
Neumann algebra for the existence of local derivations which are
not derivations on algebras of measurable operators affiliated with
Comment: 20 page
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