331 research outputs found
Jordan counterparts of Rickart and Baer -algebras, II
We introduce and investigate new classes of Jordan algebras which are close
to but wider than Rickart and Baer Jordan algebras considered in our previous
paper. Such Jordan algebras are called RJ- and BJ-algebras respectively.
Criterions are given for a Jordan algebra to be a BJ-algebra. Also, it is
proved that every finite dimensional Jordan algebra without nilpotent elements,
which have square roots, is a BJ-algebra.Comment: 10 page
2-Local Derivations on Von Neumann Algebras of Type I
In the present paper we prove that every 2-local derivation on a von Neumann
algebra of type I is a derivation.Comment: 8 page
Local derivations on finite-dimensional Lie algebras
We prove that every local derivation on a finite-dimensional semisimple Lie
algebra over an algebraically closed field of characteristic zero is a
derivation. We also give examples of finite-dimensional nilpotent Lie algebras
with which admit local derivations which
are not derivations.Comment: 14 page
-Local derivations on von Neumann algebras
The paper is devoted to the description of -local derivations on von
Neumann algebras. Earlier it was proved that every -local derivation on a
semi-finite von Neumann algebra is a derivation. In this paper, using the
analogue of Gleason Theorem for signed measures, we extend this result to type
von Neumann algebras. This implies that on arbitrary von Neumann algebra
each -local derivation is a derivation.Comment: 7 page
2-Local derivations on AW-algebras of type I
It is proved that every 2-local derivation on an AW-algebra of type I is
a derivation. Also an analog of Gleason theorem for signed measures on
projections of homogenous AW-algebras except the cases of an AW-algebra
of type I and a factor of type I, is proved.Comment: 17 page
2-local derivations on infinite-dimensional Lie algebras
The present paper is devoted to study 2-local derivations on
infinite-dimensional Lie algebras over a field of characteristic zero. We prove
that all 2-local derivations on the Witt algebra as well as on the positive
Witt algebra are (global)derivations, and give an example of
infinite-dimensional Lie algebra with a 2-local derivation which is not a
derivation.Comment: 9 page
Reversible AJW-algebras
In this article it is proved that for every special AJW-algebra there
exist central projections , , , such that (1) is
reversible and there exists a norm-closed two sided ideal of such
that ; (2) is reversible and
; (3) is a totally nonreversible AJW-algebra.Comment: 7 page
Local And 2-Local Derivations On Algebras Of Measurable Operators
The present paper presents a survey of some recent results devoted to
derivations, local derivations and 2-local derivations on various algebras of
measurable operators affiliated with von Neumann algebras. We give a complete
description of derivation on these algebras, except the case where the von
Neumann algebra is of type II. In the latter case the result is obtained
under an extra condition of measure continuity of derivations. Local and
2-local derivations on the above algebras are also considered. We give
sufficient conditions on a von Neumann algebra , under which every local or
2-local derivation on the algebra of measurable operators affiliated with
is automatically becomes a derivation. We also give examples of commutative
algebras of measurable operators admitting local and 2-local derivations which
are not derivations.Comment: accepted to Contem. Math. AMS, 21 pages. arXiv admin note: text
overlap with arXiv:0901.2983, arXiv:0808.014
Two-Local derivations on associative and Jordan matrix rings over commutative rings
In the present paper we prove that every 2-local inner derivation on the
matrix ring over a commutative ring is an inner derivation and every derivation
on an associative ring has an extension to a derivation on the matrix ring over
this associative ring. We also develop a Jordan analog of the above method and
prove that every 2-local inner derivation on the Jordan matrix ring over a
commutative ring is a derivation.Comment: 19 pages, Linear Algebra and its Applications 201
Innerness of continuous derivations on algebras of measurable operators affiliated with finite von Neumann algebras
This paper is devoted to derivations on the algebra of all measurable
operators affiliated with a finite von Neumann algebra We prove that if
is a finite von Neumann algebra with a faithful normal semi-finite trace
, equipped with the locally measure topology then every
-continuous derivation is inner. A similar result
is valid for derivation on the algebra of -measurable
operators equipped with the measure topology .Comment: Accepted for publication in the Journal of Mathematical Analysis and
Application
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